Determine what must be multiplied so that the expression below will have a common denominator. Use the backslash / to type in a fraction.

Answer:

Multiply the first fraction by [tex]\frac{x+4}{x+4}[/tex]

Multiply the second fraction by [tex]\frac{x-4}{x-4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}[/tex]

Required

Make the denominator equal

[tex]\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}[/tex]

Factorize the denominator

[tex]\frac{4}{x^2 - 4^2} + \frac{3}{x^2 + 4x + 4x+ 16}[/tex]

[tex]\frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)}[/tex]

Multiply the first fraction by [tex]\frac{x+4}{x+4}[/tex]

Multiply the second fraction by [tex]\frac{x-4}{x-4}[/tex]

[tex]\frac{x+4}{x+4} * \frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)} * \frac{x-4}{x-4}[/tex]

[tex]\frac{4(x + 4)}{(x - 4)(x + 4)(x + 4)} + \frac{3(x - 4)}{(x+ 4)(x + 4)(x - 4))}[/tex]

[tex]\frac{4(x + 4)}{(x^2 - 16)(x + 4)} + \frac{3(x - 4)}{(x^2 - 16)(x + 4))}[/tex]

The expression now have the same denominator

The grap
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