What is (x+4+3/x)/(x-4-5/x) ?

The solution to (x+4+3/x)/(x-4-5/x) is (x+3)/(x-5)

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simplify (x+4+3/x)/(x-4-5/x)

simplify

\frac{x + 4 + \frac{3}{x}}{x - 4 - \frac{5}{x}}

\frac{x + 3}{x - 5}

Solution steps

\frac{x + 4 + \frac{3}{x}}{x - 4 - \frac{5}{x}}

Join

x + 4 + \frac{3}{x} : \frac{x ^{2} + 4 x + 3}{x}

= \frac{\frac{x ^{2} + 4 x + 3}{x}}{x - 4 - \frac{5}{x}}

Join

x - 4 - \frac{5}{x} : \frac{x ^{2} - 4 x - 5}{x}

= \frac{\frac{x ^{2} + 4 x + 3}{x}}{\frac{x ^{2} - 4 x - 5}{x}}

Apply the fraction rule:

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

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

Cancel

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

= \frac{x + 3}{x - 5}

sin^{3} (x) + sin (x) cos^{2} (x)

(r cos (x))^{2}

- 4 x + 3 x

\frac{4}{3} - \frac{12}{5}

- 213 + 1913

What is (x+4+3/x)/(x-4-5/x) ?
The solution to (x+4+3/x)/(x-4-5/x) is (x+3)/(x-5)