Chapter 8: Q 8.73 (page 939)

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

Short Answer

Expert verified

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

Step by step solution

Given information

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

Simplifying the expression

The denominators of the two rational expressions are opposite so multiply the second rational expression with $\frac{- 1}{- 1} :$

$\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{(- 1) (6 y - 6)}{(- 1) (4 - y^{2})}$

Simplifying the second expression:

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

Combining the expressions:

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

Combining the like terms:

$\frac{y^{2} + y - 6}{y^{2} - 4}$

Factorizing the numerator and denominator:

$\frac{(y + 3) (y - 2)}{(y - 2) (y + 2)}$

Cancel the common terms in numerator and denominator:

$\frac{y + 3}{y + 2} .$

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

Short Answer

Step by step solution

Given information

Simplifying the expression

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Subtracty2-5yy2-4-6y-64-y2

Short Answer

Step by step solution

Given information

Simplifying the expression

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