What is (\frac{3x)/(2x)}{(x^2-81)/(x^2+11x+18)} ?

The solution to (\frac{3x)/(2x)}{(x^2-81)/(x^2+11x+18)} is (3(x+2))/(2(x-9))

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simplify (\frac{3x)/(2x)}{(x^2-81)/(x^2+11x+18)}

simplify

\frac{\frac{3 x}{2 x}}{\frac{x ^{2} - 81}{x ^{2} + 11 x + 18}}

\frac{3 ( x + 2 )}{2 ( x - 9 )}

Solution steps

\frac{\frac{3 x}{2 x}}{\frac{x ^{2} - 81}{x ^{2} + 11 x + 18}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{3 x ( x ^{2} + 11 x + 18 )}{2 x ( x ^{2} - 81 )}

Cancel the common factor:

x

= \frac{3 ( x ^{2} + 11 x + 18 )}{2 ( x ^{2} - 81 )}

Factor

x^{2} + 11 x + 18 : (x + 2) (x + 9)

= \frac{3 ( x + 2 ) ( x + 9 )}{2 ( x ^{2} - 81 )}

Factor

x^{2} - 81 : (x + 9) (x - 9)

= \frac{3 ( x + 2 ) ( x + 9 )}{2 ( x + 9 ) ( x - 9 )}

Cancel the common factor:

x + 9

= \frac{3 ( x + 2 )}{2 ( x - 9 )}

- (x - 2)

(9 - y)^{2}

(2 x - 3) 2 - 3.5 x^{2} (2 x - 5) + 6 x (2.5 x^{2} - x + 3.1)

- 3 \cdot (- 6)

8 - 52 + 6128

What is (\frac{3x)/(2x)}{(x^2-81)/(x^2+11x+18)} ?
The solution to (\frac{3x)/(2x)}{(x^2-81)/(x^2+11x+18)} is (3(x+2))/(2(x-9))