What is (9x^2)/(18x^2+90x) ?

The solution to (9x^2)/(18x^2+90x) is x/(2(x+5))

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simplify (9x^2)/(18x^2+90x)

simplify

\frac{9 x ^{2}}{18 x ^{2} + 90 x}

\frac{x}{2 ( x + 5 )}

Solution steps

\frac{9 x ^{2}}{18 x ^{2} + 90 x}

Factor

18 x^{2} + 90 x : 18 x (x + 5)

= \frac{9 x ^{2}}{18 x ( x + 5 )}

Factor the number:

18 = 9 \cdot 2

= \frac{9 x ^{2}}{9 \cdot 2 x ( x + 5 )}

Cancel the common factor:

9

= \frac{x ^{2}}{2 x ( x + 5 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{2} = xx

= \frac{xx}{2 x ( x + 5 )}

Cancel the common factor:

x

= \frac{x}{2 ( x + 5 )}

(- 3 x - 4) (x^{2} + 3 x - 5)

\frac{2}{6 x - 30} + \frac{7}{x - 5}

8 (9 t + 8) + 7 t

\frac{200}{100}

- \frac{1}{2} \cdot (- 1)