What is 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2)) ?

The solution to 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2)) is (4x^5-8x^4-5x^3+10x^2-7)/((x+1)(x-2)(x-1))

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simplify 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2))

simplify

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

\frac{4 x ^{5} - 8 x ^{4} - 5 x ^{3} + 10 x ^{2} - 7}{( x + 1 ) ( x - 2 ) ( x - 1 )}

Solution steps

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

Join

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

= 4 x^{2} - 1 + \frac{2 ( x - 1 ) - 3 ( x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )}

Convert

4 x^{2}

to fraction

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

Convert

1

to fraction

: \frac{( x + 1 ) ( x - 2 ) ( x - 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )}

= \frac{4 x ^{2} ( x + 1 ) ( x - 2 ) ( x - 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )} - \frac{( x + 1 ) ( x - 2 ) ( x - 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )} + \frac{2 ( x - 1 ) - 3 ( x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )}

Apply the fraction rule:

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

= \frac{4 x ^{2} ( x + 1 ) ( x - 2 ) ( x - 1 ) - ( x + 1 ) ( x - 2 ) ( x - 1 ) + 2 ( x - 1 ) - 3 ( x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 1 )}

Simplify

4 x^{2} (x + 1) (x - 2) (x - 1) - (x + 1) (x - 2) (x - 1) + 2 (x - 1) - 3 (x + 1) : 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} - 7

= \frac{4 x ^{5} - 8 x ^{4} - 5 x ^{3} + 10 x ^{2} - 7}{( x + 1 ) ( x - 2 ) ( x - 1 )}

(- 4 x^{3})^{2} \cdot (8 x^{4})^{- 1}

(p^{- 1} + q^{- 1})^{- 1}

4 x^{3} - 12 x - 4

(1 - 2 x) (4 + 3 x)

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

What is 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2)) ?
The solution to 4x^2-1+2/((x^2-x-2))-3/((x^2-3x+2)) is (4x^5-8x^4-5x^3+10x^2-7)/((x+1)(x-2)(x-1))