What is ((x+4)/x)/(\frac{x^2+9x+20){x^2+7x+10}} ?

The solution to ((x+4)/x)/(\frac{x^2+9x+20){x^2+7x+10}} is (x+2)/x

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simplify ((x+4)/x)/(\frac{x^2+9x+20){x^2+7x+10}}

simplify

\frac{\frac{x + 4}{x}}{\frac{x ^{2} + 9 x + 20}{x ^{2} + 7 x + 10}}

\frac{x + 2}{x}

Solution steps

\frac{\frac{x + 4}{x}}{\frac{x ^{2} + 9 x + 20}{x ^{2} + 7 x + 10}}

Apply the fraction rule:

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

= \frac{( x + 4 ) ( x ^{2} + 7 x + 10 )}{x ( x ^{2} + 9 x + 20 )}

Cancel

\frac{( x + 4 ) ( x ^{2} + 7 x + 10 )}{x ( x ^{2} + 9 x + 20 )} : \frac{x + 2}{x}

= \frac{x + 2}{x}

x^{4} - 12 x^{3} + 48 x^{2} - 64 x

2 - \frac{7}{5}

\frac{x}{3} - \frac{y}{3}

\frac{1}{28}

What is ((x+4)/x)/(\frac{x^2+9x+20){x^2+7x+10}} ?
The solution to ((x+4)/x)/(\frac{x^2+9x+20){x^2+7x+10}} is (x+2)/x