How do you subtract #\frac { 7a } { a ^ { 2} + 2a - 8} - \frac { 2} { a + 4}#?

1 Answer
Steve M
Sep 8, 2017

# (7a)/(a^2+2a-8) - 2/(a+4) = (5a+4)/((a+4)(a-2)) #

Explanation:

We wish to simplify the expression:

# E = (7a)/(a^2+2a-8) - 2/(a+4) #

Just as with numeric fractions we can deal with the expression if we use a common denominator, which in this case is the product of the two denominators, so we can write:

# E = (7a)/(a^2+2a-8) * (a+4)/(a+4) - 2/(a+4) * (a^2+2a-8)/(a^2+2a-8) #

# \ \ \ = ((7a)(a+4))/((a+4)(a^2+2a-8)) - (2(a^2+2a-8))/((a+4)(a^2+2a-8)) #

# \ \ \ = ((7a)(a+4)- 2(a^2+2a-8))/((a+4)(a^2+2a-8)) #

# \ \ \ = ((7a^2+28a - 2a^2-4a+16))/((a+4)(a+4)(a-2)) #

# \ \ \ = ((5a^2+24a+16))/((a+4)(a+4)(a-2)) #

# \ \ \ = ((5a+4)(a+4))/((a+4)(a+4)(a-2)) #

# \ \ \ = (5a+4)/((a+4)(a-2)) #

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