Rational Expression Chapter Test
Chapter
Chapter 2
Section
Rational Expression Chapter Test
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Solutions 21 Videos

Simplify the following.

(-x^2+2x + 7)+(2x^2-7x -7)

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Q1a

Simplify the following.

(2m^2-mn + 4n^2)-(5m^2-n^2)+(7m^2 -2mn)

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Q1b

Expand and simplify.

2(12a -5)(3a - 7)

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Q2a

Expand and simplify.

(2x^2y - 3xy^2)(4xy^2+5x^2y)

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Q2b

Expand and simplify.

(4x -1)(5x + 2)(x -3)

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Q2c

Expand and simplify.

(3p^2+ p - 2)^2

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Q2d

Is there a value of a such that f(x) = 9x^2 + 4 and g(x) = (3x - a)^2 are equivalent? Explain.

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Q3

If Benny is away from Candy for n consecutive days, then the amount of heartache Candy feels is given by h(n) = (2n + 1)^3.

a) If Bonnie is absent, by how much does Candy’s pain increase between day n and day n + 1?

b) How much more pain will he feel on day 6 than on day 5?

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Q4

Factor

3m(m- 1) + 2m(1 - m)

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Q5a

Factor

x^2 -27x + 72

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Q5b

Factor

15x^2 -7xy -2y^2

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Q5c

Factor

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

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Q5d

Factor

5xy - 10x -3y + 6

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Q5e

Factor

p^2 -m^2 + 6m -9

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Q5f

Use factoring to determine the x-intercepts of the curve

y =x^3 -4x^2-x + 4

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Q6

Simplify. State any restrictions on the variables.

\frac{4a^2b}{5ab^3} \div \frac{6a^2b}{35ab}

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Q7a

Simplify. State any restrictions on the variables.

\displaystyle \frac{x -2}{x^2-x -12} \times \frac{2x - 8}{x^2-4x + 4}

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Q7b

Simplify. State any restrictions on the variables.

\displaystyle \frac{5}{t^2-7t - 18} + \frac{6}{t + 2}

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Q7c

Simplify. State any restrictions on the variables.

\displaystyle \frac{4x}{6x^2 + 13x + 6} - \frac{3x}{4x^2 -9}

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Q7d

Miruo found that two rational functions each simplified to f(x) = \frac{2}{x + 1}.

Are Miruo's two rational functions equivalent? Explain.

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1.59mins
Q8

Roman thinks that he has found a simple method for determining the sum of the reciprocals of any three consecutive natural numbers. He writes, for example,

\displaystyle \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{47}{60}, \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{74}{120}, or \displaystyle \frac{37}{60}

Roman conjectures that before simplification, the numerator of the sum is three times the product of the first and third denominators, plus 2. Also, the denominator of the sum is the product of the three denominators. Is Roman’s conjecture true?

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Q9