Chapter 8: Q 178 (page 953)

Write as equivalent rational expression with LCD $(y + 7) (y + 5) (y - 6)$ of $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .

Short Answer

Expert verified

The result is $\frac{8 y - 48}{(y + 7) (y + 5) (y - 6)}, \frac{3 y^{2} + 15 y}{(y + 7) (y - 6) (y + 5)}$ .

Step by step solution

Given Information

The given expression is $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .

The LCD is $(y + 7) (y + 5) (y - 6)$ .

Factor the denominator of both expressions.

The factored form of first denominator.

$y^{2} + 12 y + 35 = (y + 7) (y + 5)$

The factored form of second denominator.

$y^{2} + y - 42 = (y + 7) (y - 6)$ .

The fractions in factored form is $\frac{8}{(y + 7) (y + 5)}, \frac{3 y}{(y + 7) (y - 6)}$ .

Compare with given LCD and multiply each denominator by the 'missing' factor and multiply each numerator by the same factor.

$\frac{8 (y - 6)}{(y + 7) (y + 5) (y - 6)}, \frac{3 y (y + 5)}{(y + 7) (y - 6) (y + 5)}$

Simplify the numerators.

Multiply the numerator using distributive property.

\frac{8 y - 48}{(y + 7) (y + 5) (y - 6)}, \frac{3 y^{2} + 15 y}{(y + 7) (y - 6) (y + 5)}

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Write as equivalent rational expression with LCD $(y + 7) (y + 5) (y - 6)$ of $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .

Short Answer

Step by step solution

Given Information

Factor the denominator of both expressions.

Compare with given LCD and multiply each denominator by the 'missing' factor and multiply each numerator by the same factor.

Simplify the numerators.

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Write as equivalent rational expression with LCD(y+7)(y+5)(y-6)of8y2+12y+35,3yy2+y-42.

Short Answer

Step by step solution

Given Information

Factor the denominator of both expressions.

Compare with given LCD and multiply each denominator by the 'missing' factor and multiply each numerator by the same factor.

Simplify the numerators.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Mechanics Maths

Logic and Functions

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write as equivalent rational expression with LCD $(y + 7) (y + 5) (y - 6)$ of $\frac{8}{y^{2} + 12 y + 35}, \frac{3 y}{y^{2} + y - 42}$ .