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Chapter 7: Problem 42

Add or subtract as indicated. Simplify the result, if possible. $$\frac{8 y}{y^{2}-16}-\frac{5}{y+4}$$

Short Answer

Expert verified
The simplified expression from the given exercise is \(\frac{3y+20}{(y-4)(y+4)}\)

Step by step solution

01

Identify the Difference of Squares

The denominator of the first fraction, \(y^{2}-16\), is a difference of perfect squares, which can be factored as \((y-4)(y+4)\).
02

Rewrite the first fraction

Rewrite the first fraction using the new denominator. The fraction becomes: \[\frac{8y}{(y-4)(y+4)}\].
03

Find a common denominator

To subtract fractions, a common denominator is needed. In this case, the common denominator should be \((y-4)(y+4)\), which is achieved by writing the second fraction as \[\frac{5(y-4)}{(y-4)(y+4)}]\].
04

Subtract the fractions

Subtract the fractions by subtracting the numerators while keeping the common denominator as is: \[\frac{8y-5(y-4)}{(y-4)(y+4)}\].
05

Simplify the expression

Simplify the expression by distributing the -5 in the numerator: \[\frac{8y-5y+20}{(y-4)(y+4)}=\frac{3y+20}{(y-4)(y+4)}\]

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. a. If \(y=k x\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

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