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kupik [55]
3 years ago
8

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

fraction.

Mathematics
1 answer:
Mashutka [201]3 years ago
7 0

Answer:

Multiply the first fraction by \frac{x+4}{x+4}

Multiply the second fraction by \frac{x-4}{x-4}

Step-by-step explanation:

Given

\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}

Required

Make the denominator equal

\frac{4}{x^2 - 16} + \frac{3}{x^2 + 8x + 16}

Factorize the denominator

\frac{4}{x^2 - 4^2} + \frac{3}{x^2 + 4x + 4x+ 16}

\frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)}

Multiply the first fraction by \frac{x+4}{x+4}

Multiply the second fraction by \frac{x-4}{x-4}

\frac{x+4}{x+4} * \frac{4}{(x - 4)(x + 4)} + \frac{3}{(x+ 4)(x + 4)} * \frac{x-4}{x-4}

\frac{4(x + 4)}{(x - 4)(x + 4)(x + 4)} + \frac{3(x - 4)}{(x+ 4)(x + 4)(x - 4))}

\frac{4(x + 4)}{(x^2 - 16)(x + 4)} + \frac{3(x - 4)}{(x^2 - 16)(x + 4))}

<em>The expression now have the same denominator</em>

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