How do you multiply and simplify $\frac { c + 1} { c ^ { 2} - 4} \cdot \frac { c ^ { 2} - 4} { c ^ { 2} + 2c + 1}$ ?

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Answer 1 · 2017-05-26T02:11:06

See a solution process below:

First, cancel like terms in the numerator and denominator of the fractions:

$(c + 1)/color(red)(cancel(color(black)(c^2 - 4))) * color(red)(cancel(color(black)(c^2 - 4)))/(c^2 + 2c + 1) =>$

$(c + 1)/(c^2 + 2c + 1)$

Next, factor the denominator as:

$(c + 1)/((c + 1)(c + 1))$

Now, again, cancel common terms in the numerator and denominator:

$color(red)(cancel(color(black)(c + 1)))/(color(red)(cancel(color(black)((c + 1))))(c + 1)) =>$

$1/(c + 1)$

How do you multiply and simplify \frac { c + 1} { c ^ { 2} - 4} \cdot \frac { c ^ { 2} - 4} { c ^ { 2} + 2c + 1}\frac { c + 1} { c ^ { 2} - 4} \cdot \frac { c ^ { 2} - 4} { c ^ { 2} + 2c + 1}?