First, factor the numerator and denominator:
Numerator: x^2 + 2x + 1 = (x + 1)^2
Denominator: x^2 - 1 = (x + 1)(x - 1)
Numerator of whole fraction: (x + 1)^2 / (x - 2)
Denominator of whole fraction: (x + 1)(x - 1) / (x + 2)(x - 2)
To divide by a fraction, you invert and multiply. Therefore:
(x + 1)^2 / (x - 2) * (x + 2)(x - 2) / (x + 1)(x - 1)
Simplify:
(x + 1)(x + 2) / (x - 1)
Therefore, the answer is A. Start Fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x minus 1 End Fraction.
Divide. start fraction start fraction x squared plus 2 x plus 1 over x minus 2 end fraction over start fraction x squared minus 1 over x squared minus 4 end fraction end fraction
A. Start Fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x minus 1 End Fraction
B. Start Fraction left-parenthesis lower x minus 1 right-parenthesis left-parenthesis lower x minus 2 right-parenthesis over lower x plus 1 End Fraction
C. Start Fraction left-parenthesis lower x minus 1 right-parenthesis left-parenthesis lower x plus 2 right-parenthesis over lower x plus 1 End Fraction
D. Start Fraction left-parenthesis lower x plus 1 right-parenthesis left-parenthesis lower x minus 2 right-parenthesis over lower x minus 1 End Fraction
1 answer