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# express as a single fraction

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(8/x-4) + (5/x^2 + 2x -24)

Aug 8, 2017

#1
+7350
+3

Express     $$\frac8{x-4}+\frac5{x^2+2x-24}$$     as a single fraction.

$$\frac8{x-4}+\frac5{x^2+2x-24}$$

Factor the denominator of the second fraction.

What two numbers add to  2  and multiply to  -24 ?→  +6  and  -4  .

=  $$\frac8{x-4}+\frac5{(x+6)(x-4)}$$

Multiply the first fraction by $$\frac{x+6}{x+6}$$  .

=  $$(\frac{x+6}{x+6})(\frac8{x-4})+\frac5{(x+6)(x-4)}$$

=  $$\frac{8x+48}{(x+6)(x-4)}+\frac5{(x+6)(x-4)}$$

Now there's a common denominator so we can add the fractions.

=  $$\frac{8x+48+5}{(x+6)(x-4)}$$

=  $$\frac{8x+53}{(x+6)(x-4)}$$

.
Aug 8, 2017

#1
+7350
+3

Express     $$\frac8{x-4}+\frac5{x^2+2x-24}$$     as a single fraction.

$$\frac8{x-4}+\frac5{x^2+2x-24}$$

Factor the denominator of the second fraction.

What two numbers add to  2  and multiply to  -24 ?→  +6  and  -4  .

=  $$\frac8{x-4}+\frac5{(x+6)(x-4)}$$

Multiply the first fraction by $$\frac{x+6}{x+6}$$  .

=  $$(\frac{x+6}{x+6})(\frac8{x-4})+\frac5{(x+6)(x-4)}$$

=  $$\frac{8x+48}{(x+6)(x-4)}+\frac5{(x+6)(x-4)}$$

Now there's a common denominator so we can add the fractions.

=  $$\frac{8x+48+5}{(x+6)(x-4)}$$

=  $$\frac{8x+53}{(x+6)(x-4)}$$

hectictar Aug 8, 2017