Mathematics: Find the difference. (9/x^2-9x)-(6/x^2-81)

Find the difference. (9/x^2-9x)-(6/x^2-81) - id92962815176385, monstax6

maddison788

19.01.2022

The difference is $\frac{3 x+81}{x(x-9)(x+9)}$

Explanation:

The expression is $\left(\frac{9}{x^{2}-9 x}\right)-\left(\frac{6}{x^{2}-81}\right)$

Removing the parenthesis, we have,

$\left\frac{9}{x^{2}-9 x}\right-\left\frac{6}{x^{2}-81}\right$

Factoring the terms $x^{2}-9 x$ and $x^{2}-81$ , we get,

$\frac{9}{x(x-9)}-\frac{6}{(x+9)(x-9)}$

Taking LCM, we get,

$\frac{9(x+9)-6x}{x(x-9)(x+9)}}$

Simplifying the numerator, we get,

$\frac{9x+81-6x}{x(x-9)(x+9)}}$

Subtracting the numerator, we have,

$\frac{3 x+81}{x(x-9)(x+9)}$

Hence, the difference is $\frac{3 x+81}{x(x-9)(x+9)}$

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