Master Rational Expressions: Enhance Your Math Skills for Biology

Question 1

Multiply the rational expressions: (a + b) / (a - b) * (a - b) / (a + b).

Accepted Answer

1

Answer

-1

Answer

a - b

Answer

a + b

Question 2

Simplify the rational expression: (x^2 - 4) / (x^2 + 2x + 4) * (x + 2) / (x - 2).

Accepted Answer

1

Answer

-1

Answer

x

Answer

-x

Question 3

Multiply the rational expressions: (a^2 - 9b^2) / (a + 3b) * (a - 3b) / (a^2 - 9b^2).

Accepted Answer

1

Answer

-1

Answer

a + 3b

Answer

a - 3b

Question 4

Simplify the rational expression: (x² - 4) / (x - 2)

Accepted Answer

x - 2

Answer

x + 2

Answer

x² + 2

Answer

x² - 2

Question 5

Multiply the rational expressions: (x + 3) / (x - 2) * (x - 2) / (x + 1)

Accepted Answer

1

Answer

x + 1

Answer

x - 1

Answer

x

Question 6

Find the domain of the rational expression: (x² - 4) / (x - 2)

Accepted Answer

All real numbers except 2

Answer

All real numbers

Answer

All positive real numbers

Answer

All rational numbers except 2

Question 7

Evaluate the rational expression: (x² - 9) / (x + 3) for x = 4

Accepted Answer

5

Answer

-5

Answer

1

Answer

-1

Question 8

Which of the following is an example of an improper rational expression?

Accepted Answer

x^2 + 1 / x

Answer

x / (x + 1)

Answer

1 / x

Answer

x - 1 / x + 2

Question 9

Simplify the expression: ((x^3 - y^3) / (x - y)) - ((x^2 + xy + y^2) / (x + y))

Accepted Answer

2xy - y^2

Answer

2xy + y^2

Answer

x^2 - xy + y^2

Answer

x^2 + xy + y^2

Question 10

Simplify the complex fraction: (2 / (x - 1)) / (3 / (x + 1))

Accepted Answer

2(x + 1) / 3(x - 1)

Answer

3(x - 1) / 2(x + 1)

Answer

2(x - 1) / 3(x + 1)

Answer

3(x + 1) / 2(x - 1)

Question 11

Which of the following is NOT a restriction on the variable in a rational expression?

Accepted Answer

Variable cannot be negative

Answer

Denominator cannot be zero

Answer

Numerator cannot be zero

Answer

Variable cannot be undefined

Question 12

Multiply the rational expressions: ((x - 1) / (x + 2)) * ((x + 2) / (x - 1))

Accepted Answer

1

Answer

x

Answer

x - 1

Answer

x + 2

Question 13

Simplify the rational expression: (x - 2)/(x + 3).

Accepted Answer

(x - 2)/(x + 3)

Answer

(x - 5)/(x + 3)

Answer

(x - 2)/x

Answer

(x - 3)/x

Question 14

Which of the following rational expressions is undefined?

Accepted Answer

(x - 3)/(x^2 + 1)

Answer

(x - 1)/(x + 2)

Answer

(x + 2)/(x - 1)

Answer

(x^2 + 1)/(x - 3)

Question 15

Find the domain of the rational expression: (x^2 - 4)/(x - 2).

Accepted Answer

{x | x ≠ 2}

Answer

{x | x ≠ -2}

Answer

{x | x ≠ ±2}

Answer

All real numbers

Question 16

Find the least common multiple (LCM) of the following rational expressions: (rac{x + 3}{x - 1}) and (rac{x - 3}{x + 1})

Accepted Answer

((x - 1)(x + 1))

Answer

(x - 3)

Answer

(x + 3)

Answer

The expressions have no LCM

Question 17

Solve: (x - 1)/(x + 2) = 2/(x - 3).

Accepted Answer

x = 11

Answer

x = -11

Answer

x = 5

Answer

x = -5

Question 18

Find the least common denominator (LCD) of [(x - 1)/(x^2 - 4)] and [(2)/(x + 2)]

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 1)(x + 2)

Answer

(x - 2)^2

Answer

(x + 2)^2

Question 19

Which rational expression is equivalent to y = 2x + 1?

Accepted Answer

(2x + 1)/(x + 1)

Answer

(2x + 1)/(x - 1)

Answer

(2x - 1)/(x - 1)

Answer

(2x - 1)/(x + 1)

Question 20

Simplify the rational expression: (x^2 + 5x - 6) / (x - 2)

Accepted Answer

(x + 6)

Answer

(x - 6)

Answer

(x^2 + 6)

Answer

(x^2 - 6)

Question 21

Find the domain of the rational expression: (x - 3) / (x^2 - 9)

Accepted Answer

All real numbers except x = ±3

Answer

x ≠ 0

Answer

All real numbers

Answer

x > 3 or x < -3

Question 22

Simplify the following radical expression: (sqrt(x) + 1) / (sqrt(x) - 1)

Accepted Answer

(x + 1) / (x - 1)

Answer

(sqrt(x) + 1)^2

Answer

(sqrt(x) - 1)^2

Question 23

Identify the excluded value(s) for the rational expression: (x^2 - 4) / (x - 2)

Accepted Answer

2

Answer

0

Answer

-2

Question 24

Which of the following rational expressions is in lowest terms?

Accepted Answer

(x - 1) / (x + 1)

Answer

(x^2 - 4) / (x^2 - 2x + 4)

Answer

(x^2 - 1) / (x^2 + 1)

Answer

(x - 2) / (x + 2)

Question 25

Simplify the rational expression: (6x^2 - 12x) / (3x)

Accepted Answer

2x - 4

Answer

2x^2 - 4x

Answer

2x + 4

Answer

6x - 12

Question 26

What is the least common denominator (LCD) of the fractions (x + 2) / (x^2 - 4) and 3 / (x - 2)?

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 2)

Answer

(x^2 - 4)(x - 2)

Answer

(x - 2)

Question 27

A bacterial population doubles every hour. If there are initially 100 bacteria, which rational expression represents the population after 't' hours?

Accepted Answer

100 * 2^t

Answer

100 / 2^t

Answer

200^t

Answer

100 + 2t

Question 28

The rate of an enzyme-catalyzed reaction is given by the expression: (Vmax * [S]) / (Km + [S]), where Vmax is the maximum rate, [S] is the substrate concentration, and Km is the Michaelis constant. If Vmax = 100 µM/s and Km = 10 µM, what is the rate when [S] = 20 µM?

Accepted Answer

66.67 µM/s

Answer

200 µM/s

Answer

100 µM/s

Answer

50 µM/s

Question 29

Which value(s) of x make the expression (x - 5) / (x^2 - 16) undefined?

Accepted Answer

x = 4 and x = -4

Answer

x = 5

Answer

x = -4

Answer

x = 4

Question 30

Simplify the rational expression: (x^2 - 4) / (x + 2)

Accepted Answer

x - 2

Answer

(x - 2)(x + 2)

Answer

x^2 - 2

Answer

x + 2

Question 31

Multiply the rational expressions: (x + 3) / (x - 1) * (x^2 - 1) / (x^2 + 5x + 6)

Accepted Answer

(x + 1) / (x + 2)

Answer

(x - 1) / (x + 2)

Answer

(x + 3) / (x + 2)

Answer

(x + 1) / (x - 2)

Question 32

Divide the rational expressions: (x^2 - 9) / (x + 4) ÷ (x - 3) / (x^2 + 8x + 16)

Accepted Answer

(x + 3)(x + 4) / (x - 3)

Answer

(x + 3)(x - 4) / (x - 3)

Answer

(x - 3)(x + 4) / (x + 3)

Answer

(x - 3)(x + 4) / (x + 3)

Question 33

Find the Least Common Multiple (LCM) of the following expressions: 2x, x^2 - 4, and x + 2

Accepted Answer

2x(x + 2)(x - 2)

Answer

2(x + 2)(x - 2)

Answer

2x(x + 2)

Answer

x(x + 2)(x - 2)

Question 34

Add the rational expressions: 3 / (x - 1) + 2 / (x + 1)

Accepted Answer

(5x + 1) / (x^2 - 1)

Answer

(5x + 1) / (x^2 + 1)

Answer

(5x - 1) / (x^2 - 1)

Answer

(5x - 1) / (x^2 + 1)

Question 35

Subtract the rational expressions: (x^2 + 2x - 3) / (x^2 - 1) - (x - 1) / (x + 1)

Accepted Answer

2 / (x - 1)

Answer

2 / (x + 1)

Answer

1 / (x + 1)

Answer

1 / (x - 1)

Question 36

Solve the rational equation: 2 / (x - 3) = 1 / (x + 1)

Accepted Answer

x = 1

Answer

x = 3

Answer

x = -1

Answer

x = -3

Question 37

Identify the excluded values for the rational expression: (x - 2) / (x^2 - 9)

Accepted Answer

x = 3, x = -3

Answer

x = -2

Answer

x = 2

Answer

x = 3

Question 38

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the area of the garden expressed as a rational expression?

Accepted Answer

(x + 5)(x - 2) square meters

Answer

(x + 5) + (x - 2) square meters

Answer

(x + 5) / (x - 2) square meters

Answer

(x + 5) - (x - 2) square meters

Question 39

The speed of a boat in still water is (x + 2) km/h. If the boat travels upstream against a current of 3 km/h, what is the speed of the boat upstream, expressed as a rational expression?

Accepted Answer

(x - 1) km/h

Answer

(x + 2) + 3 km/h

Answer

(x + 2) / 3 km/h

Answer

(x + 5) km/h