What is (x^4+2x^3-3x^2)/(x^4+2x^3+2x^2+10x-15) ?

The solution to (x^4+2x^3-3x^2)/(x^4+2x^3+2x^2+10x-15) is (x^2)/(x^2+5)

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simplify (x^4+2x^3-3x^2)/(x^4+2x^3+2x^2+10x-15)

simplify

\frac{x ^{4} + 2 x ^{3} - 3 x ^{2}}{x ^{4} + 2 x ^{3} + 2 x ^{2} + 10 x - 15}

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

Solution steps

\frac{x ^{4} + 2 x ^{3} - 3 x ^{2}}{x ^{4} + 2 x ^{3} + 2 x ^{2} + 10 x - 15}

Factor

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

= \frac{x ^{2} ( x - 1 ) ( x + 3 )}{x ^{4} + 2 x ^{3} + 2 x ^{2} + 10 x - 15}

Factor

x^{4} + 2 x^{3} + 2 x^{2} + 10 x - 15 : (x - 1) (x + 3) (x^{2} + 5)

= \frac{x ^{2} ( x - 1 ) ( x + 3 )}{( x - 1 ) ( x + 3 ) ( x ^{2} + 5 )}

Cancel the common factor:

x - 1

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

Cancel the common factor:

x + 3

= \frac{x ^{2}}{x ^{2} + 5}

7 + 3 (1 - 2 x)

8 1^{4}

- 227 - 7147

(- 10 x^{2} - x + 6) + (10 x^{2} - 5)

What is (x^4+2x^3-3x^2)/(x^4+2x^3+2x^2+10x-15) ?
The solution to (x^4+2x^3-3x^2)/(x^4+2x^3+2x^2+10x-15) is (x^2)/(x^2+5)