What is ((x+3))/((x^2-x-2))+((x-1))/((x^2+2x+1)) ?

The solution to ((x+3))/((x^2-x-2))+((x-1))/((x^2+2x+1)) is (2x^2+x+5)/((x+1)^2(x-2))

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simplify ((x+3))/((x^2-x-2))+((x-1))/((x^2+2x+1))

simplify

\frac{( x + 3 )}{( x ^{2} - x - 2 )} + \frac{( x - 1 )}{( x ^{2} + 2 x + 1 )}

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

Solution steps

\frac{x + 3}{x ^{2} - x - 2} + \frac{x - 1}{x ^{2} + 2 x + 1}

Least Common Multiplier of

x^{2} - x - 2, x^{2} + 2 x + 1 : (x + 1)^{2} (x - 2)

Adjust Fractions based on the LCM

= \frac{( x + 3 ) ( x + 1 )}{( x + 1 ) ^{2} ( x - 2 )} + \frac{( x - 1 ) ( x - 2 )}{( x + 1 ) ^{2} ( x - 2 )}

Apply the fraction rule:

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

= \frac{( x + 3 ) ( x + 1 ) + ( x - 1 ) ( x - 2 )}{( x + 1 ) ^{2} ( x - 2 )}

Simplify

(x + 3) (x + 1) + (x - 1) (x - 2) : 2 x^{2} + x + 5

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

\frac{1 + tan ^{2} ( x )}{cos ^{2} ( x )}

12 x^{2} - 27 y^{2} + 10 x + 15 y

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

10 x^{3} \cdot y^{1} - 3 x^{3} \cdot y^{4}

(6) 5 (n + 21)

What is ((x+3))/((x^2-x-2))+((x-1))/((x^2+2x+1)) ?
The solution to ((x+3))/((x^2-x-2))+((x-1))/((x^2+2x+1)) is (2x^2+x+5)/((x+1)^2(x-2))