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

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

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

simplify

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

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

Solution steps

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 2)^{2} = (x - 2) (x - 2)

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

Cancel the common factor:

x - 2

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

- sin (x) \cdot sin (x)

- f (x)

1 \cdot x^{2}

(a + b) 3

- 8 \cdot (- 4)

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