How do you subtract #\frac { 1} { x + 8} - \frac { 1} { x + 6}#?

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Answer 1 · 2016-11-04T17:14:14

Please see the explanation for the steps leading to the answer:
#(-2)/((x + 6)(x + 8))#

Given:
#1/(x + 8) - 1/(x + 6) = ?#

Make a common denominator by multiplying, the first term by 1 in the form of #(x + 6)/(x + 6)#, and the second by 1 in the form of #(x + 8)/(x + 8)#

#1/(x + 8)((x +6)/(x + 6)) - 1/(x + 6)((x + 8)/(x + 8)) = #

Multiply the numerators and denominators:

#(x +6)/((x + 8)(x + 6)) - (x + 8)/((x + 6)(x + 8)) = #

Combine over 1 denominator:

#((x +6) - (x + 8))/((x + 6)(x + 8)) = #

Use the distributive property on the second term of the numerator:

#(x +6 -x - 8)/((x + 6)(x + 8)) = #

Combine like terms:

#(-2)/((x + 6)(x + 8))#