Chapter 8: Q 183 (page 953)

Write as equivalent rational expression with LCD $(d + 5) (3 d - 1) (d - 6)$ of $\frac{2}{3 d^{2} + 14 d - 5}, \frac{5 d}{3 d^{2} - 19 d + 6}$ .

Short Answer

Expert verified

The result is $\frac{2 d - 12}{(d + 5) (3 d - 1) (d - 6)}, \frac{5 d^{2} + 25 d}{(d + 5) (3 d - 1) (d - 6)}$ .

Step by step solution

Given Information

The given expression is $\frac{2}{3 d^{2} + 14 d - 5}, \frac{5 d}{3 d^{2} - 19 d + 6}$ .

The LCD is $(d + 5) (3 d - 1) (d - 6)$ .

Factor the denominator of both expressions.

The factored form of first denominator.

$3 d^{2} + 14 d - 5 = (d + 5) (3 d - 1)$

The factored form of second denominator.

$3 d^{2} - 19 d + 6 = (d - 6) (3 d - 1)$

The fractions in factored form is $\frac{2}{(d + 5) (3 d - 1)}, \frac{5 d}{(d - 6) (3 d - 1)}$ .

Multiply each denominator by the 'missing' factor and multiplyeach numerator by the same factor.

$\frac{2 (d - 6)}{(d + 5) (3 d - 1) (d - 6)}, \frac{5 d (d + 5)}{(d - 6) (3 d - 1) (d + 5)}$

Simplify the numerators.

Multiply the numerator using distributive property.

$\frac{2 d - 12}{(d + 5) (3 d - 1) (d - 6)}, \frac{5 d^{2} + 25 d}{(d + 5) (3 d - 1) (d - 6)}$ .

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Write as equivalent rational expression with LCD $(d + 5) (3 d - 1) (d - 6)$ of $\frac{2}{3 d^{2} + 14 d - 5}, \frac{5 d}{3 d^{2} - 19 d + 6}$ .

Short Answer

Step by step solution

Given Information

Factor the denominator of both expressions.

Multiply each denominator by the 'missing' factor and multiplyeach numerator by the same factor.

Simplify the numerators.

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Write as equivalent rational expression with LCD(d+5)(3d-1)(d-6)of23d2+14d-5,5d3d2-19d+6.

Short Answer

Step by step solution

Given Information

Factor the denominator of both expressions.

Multiply each denominator by the 'missing' factor and multiplyeach 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

Theoretical and Mathematical Physics

Calculus

Pure Maths

Applied Mathematics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write as equivalent rational expression with LCD $(d + 5) (3 d - 1) (d - 6)$ of $\frac{2}{3 d^{2} + 14 d - 5}, \frac{5 d}{3 d^{2} - 19 d + 6}$ .