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Carolyn C. for tutoring lessons in Fair Lawn NJ WyzAnt Tutoring Tutor Tutor United States

Carolyn C.

Tutor, Mentor and Accomplished Mathematician

Fair Lawn, NJ (07410)

Travel Radius 10 miles
Hourly Fee $120.00
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Carolyn's Responses in WyzAnt Answers

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Algebra 1Adding

a/a+1 -1/a-1

adding and subtracting with unlike denominators

+ more- less
Asked by Haley from Wildomar, CA
10

Carolyn's Answer:

Just like any other adding and subtracting with unlike denominators, you need to find the least common denominator. In this case, the LCD is just the multiple of the denominators. So multiply both the top and bottom of a/a+1 by (a-1) and multiply both the top and bottom of 1/a-1 by (a+1) to get:

(a/a+1)*(a-1/a-1) - (1/a-1)*(a+1)/(a+1)

= a(a-1)/(a+1)(a-1) - (a+1)/(a+1)(a-1)

Then combine the numerators:

= a(a-1)-(a+1) / (a-1)(a+1)

Distribute and simplify the numerator to get:

a2 - a - a - 1 / (a-1)(a+1)

= a2 - 2a  - 1 / (a-1)(a+1)

Factor the numerator:

= (a-1)(a-1) / (a-1)(a+1) 

(a-1) in both numerator and denominator cancels out:

= (a-1)/(a+1)

Carolyn's Hourly Rate

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