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Arturiano [62]
2 years ago
8

Simplify

" align="absmiddle" class="latex-formula"> ÷ \frac{9X}{x^{2}- 9x -10}
Mathematics
1 answer:
mr Goodwill [35]2 years ago
4 0

In the second fraction, factorize the denominator:

x^2-9x-10=(x-10)(x+1)

Then we have, as long as x\neq10,

\dfrac1{x-10}\div\dfrac{9x}{x^2-9x-10}=\dfrac{\frac1{x-10}}{\frac{9x}{(x-10)(x+1)}}=\dfrac1{\frac{9x}{x+1}}=\dfrac{x+1}{9x}

which you could also write as

\dfrac{x+1}{9x}=\dfrac x{9x}+\dfrac1{9x}=\dfrac19+\dfrac1{9x}

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