What is (x+5)/(x+2)-(x+1)/(x^2+2x) ?

The solution to (x+5)/(x+2)-(x+1)/(x^2+2x) is (x^2+4x-1)/(x(x+2))

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simplify (x+5)/(x+2)-(x+1)/(x^2+2x)

simplify

\frac{x + 5}{x + 2} - \frac{x + 1}{x ^{2} + 2 x}

\frac{x ^{2} + 4 x - 1}{x ( x + 2 )}

Solution steps

\frac{x + 5}{x + 2} - \frac{x + 1}{x ^{2} + 2 x}

Least Common Multiplier of

x + 2, x^{2} + 2 x : x (x + 2)

Adjust Fractions based on the LCM

= \frac{( x + 5 ) x}{x ( x + 2 )} - \frac{x + 1}{x ( x + 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{( x + 5 ) x - ( x + 1 )}{x ( x + 2 )}

Simplify

(x + 5) x - (x + 1) : x^{2} + 4 x - 1

= \frac{x ^{2} + 4 x - 1}{x ( x + 2 )}

\frac{3 s ^{2}}{4 ( s ) ^{3}}

\frac{x ^{2} - 5 x - 6}{x ^{2} + 2 x + 1}

6 \cdot (- \frac{1}{3})

25 + 710 - 320

lo g_{10} (2) (2)

What is (x+5)/(x+2)-(x+1)/(x^2+2x) ?
The solution to (x+5)/(x+2)-(x+1)/(x^2+2x) is (x^2+4x-1)/(x(x+2))