What is (x^2-1)/(x^2-3x+2)*(x^3-2x^2)/(7x+7) ?

The solution to (x^2-1)/(x^2-3x+2)*(x^3-2x^2)/(7x+7) is (x^2)/7

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simplify (x^2-1)/(x^2-3x+2)*(x^3-2x^2)/(7x+7)

simplify

\frac{x ^{2} - 1}{x ^{2} - 3 x + 2} \cdot \frac{x ^{3} - 2 x ^{2}}{7 x + 7}

\frac{x ^{2}}{7}

Solution steps

\frac{x ^{2} - 1}{x ^{2} - 3 x + 2} \cdot \frac{x ^{3} - 2 x ^{2}}{7 x + 7}

Cancel

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

= \frac{x + 1}{x - 2} \cdot \frac{x ^{3} - 2 x ^{2}}{7 x + 7}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( x + 1 ) ( x ^{3} - 2 x ^{2} )}{( x - 2 ) ( 7 x + 7 )}

Factor

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

= \frac{( x + 1 ) x ^{2} ( x - 2 )}{( x - 2 ) ( 7 x + 7 )}

Cancel the common factor:

x - 2

= \frac{( x + 1 ) x ^{2}}{7 x + 7}

Factor

7 x + 7 : 7 (x + 1)

= \frac{( x + 1 ) x ^{2}}{7 ( x + 1 )}

Cancel the common factor:

x + 1

= \frac{x ^{2}}{7}

2 \frac{5}{7}

lo g_{10} (0.002)

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

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

lo g_{10} (0.7)

What is (x^2-1)/(x^2-3x+2)*(x^3-2x^2)/(7x+7) ?
The solution to (x^2-1)/(x^2-3x+2)*(x^3-2x^2)/(7x+7) is (x^2)/7