How do you multiply \(\frac{x^2 - 4}{x^2 - 1}\) by \(\frac{x + 1}{x^2 + 2x}\)?
Answer (3)
x 2 − 1 x 2 − 4 ∗ x 2 + 2 x x + 1 = x 2 − 1 x 2 − 2 2 ∗ x ( x + 2 ) x + 1 = = ( x − 1 ) ( x + 1 ) 1 ( x − 2 ) ( x + 2 ) 1 ∗ x ( x + 2 ) 1 ( x + 1 ) 1 = x ( x − 1 ) x − 2 a 2 − b 2 = ( a − b ) ( a + b )
(X2-4)/(x2-1). * (x+1)/(x2+2x) [(x-2)(x+2)]/[(x-1)(x+1)]. * (x+1)[x(x+2)] (x-2)/(x-1) * 1/x (x-2)/(x2-x)
To multiply x 2 − 1 x 2 − 4 by x 2 + 2 x x + 1 , first factor the polynomials in the numerators and denominators, then multiply the fractions, and finally cancel any common factors. After simplification, the result is x ( x − 1 ) x − 2 . Be mindful of values for x that would make the original expression undefined.
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