Q. 7.29 Subtract:y2-5yy2-4-6y-64-y2... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 7.29 (page 658)

Subtract:
$\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}}$

Short Answer

Expert verified

The required result is $\frac{y + 3}{y + 2}$ .

Step by step solution

Step 1. Given information

The given polynomial is $\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}}$ .

Step 2. Multiply the second term by -1-1

Multiply the numerator and denominator of the second term by $- 1$ .

$\begin{array}{rcl} \frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}} & = & \frac{y^{2} - 5 y}{y^{2} - 4} - \frac{- 1 (6 y - 6)}{- 1 (4 - y^{2})} \\ = & \frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 - 6 y}{y^{2} - 4} \end{array}$

Step 3. Subtract the Numerators

As the denominator is same for both the terms, add the numerator and place over the common denominator.
Add the like terms of the numerator.

$\begin{array}{rcl} \frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 - 6 y}{y^{2} - 4} & = & \frac{y^{2} - 5 y - (6 - 6 y)}{y^{2} - 4} \\ = & \frac{y^{2} - 5 y - 6 + 6 y}{y^{2} - 4} \\ = & \frac{y^{2} + y - 6}{y^{2} - 4} \end{array}$

Step 4. Factor the Numerator

Factor the expression in the numerator and then cancel out the common terms from numerator and denominator.

$\begin{array}{rcl} \frac{y^{2} + y - 6}{y^{2} - 4} & = & \frac{(y + 3) (y - 2)}{(y + 2) (y - 2)} \\ = & \frac{(y + 3) (y - 2)}{(y + 2) (y - 2)} \\ = & \frac{y + 3}{y + 2} \end{array}$

So, the resultant expression is $\frac{y + 3}{y + 2}$ .

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91影视

Subtract:
$\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Multiply the second term by -1-1

Step 3. Subtract the Numerators

Step 4. Factor the Numerator

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