What is (3x^2+3x-6)/(6(x^2-2x+1)) ?

The solution to (3x^2+3x-6)/(6(x^2-2x+1)) is (x+2)/(2(x-1))

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simplify (3x^2+3x-6)/(6(x^2-2x+1))

simplify

\frac{3 x ^{2} + 3 x - 6}{6 ( x ^{2} - 2 x + 1 )}

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

Solution steps

\frac{3 x ^{2} + 3 x - 6}{6 ( x ^{2} - 2 x + 1 )}

Factor

3 x^{2} + 3 x - 6 : 3 (x^{2} + x - 2)

= \frac{3 ( x ^{2} + x - 2 )}{6 ( x ^{2} - 2 x + 1 )}

Factor

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

= \frac{3 ( x - 1 ) ( x + 2 )}{6 ( x ^{2} - 2 x + 1 )}

Factor the number:

6 = 3 \cdot 2

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

Cancel the common factor:

3

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

Factor

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

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

Apply exponent rule:

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

(x - 1)^{2} = (x - 1) (x - 1)

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

Cancel the common factor:

x - 1

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

\frac{1}{i} + \frac{3 + 2 i}{2 - i}

x^{- a}

\frac{- \frac{4}{5}}{- \frac{3}{5}}

- \frac{4}{- 8}

(y^{5})^{2}

What is (3x^2+3x-6)/(6(x^2-2x+1)) ?
The solution to (3x^2+3x-6)/(6(x^2-2x+1)) is (x+2)/(2(x-1))