SOLUTION: Add or subtract the fractions. Express the answer in simplest form: A: [4/(x-2)]+[3/x^2-x-2] B: [4y/(y^2+6y+5)]-[2y/(y^2-1)]

Algebra ->  Equations -> SOLUTION: Add or subtract the fractions. Express the answer in simplest form: A: [4/(x-2)]+[3/x^2-x-2] B: [4y/(y^2+6y+5)]-[2y/(y^2-1)]      Log On


   

Question 147022: Add or subtract the fractions. Express the answer in simplest form:
A: [4/(x-2)]+[3/x^2-x-2]
B: [4y/(y^2+6y+5)]-[2y/(y^2-1)]
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A: %284%2F%28x-2%29%29%2B%283%2F%28x%5E2-x-2%29%29+
Remember, to add or subtract fractions you need a common denominator.
Luckily,
x%5E2-x-2=%28x-2%29%28x%2B1%29
So you can multiply, the first term by (x+1)/(x+1) to get it done.
A: %284%2F%28x-2%29%29%2B%283%2F%28x%5E2-x-2%29%29+
A: %284%28x%2B1%29%2F%28%28x-2%29%2A%28x%2B1%29%29%29%2B%283%2F%28%28x-2%29%2A%28x%2B1%29%29%29
A: %284x%2B4%2B3%29%2F%28%28x-2%29%2A%28x%2B1%29%29+
A: %284x%2B7%29%2F%28%28x-2%29%2A%28x%2B1%29%29+
B: 4y%2F%28y%5E2%2B6y%2B5%29-2y%2F%28y%5E2-1%29
Let's look at both denominators and factor them.
First term denominator:
y%5E2%2B6y%2B5=%28y%2B5%29%28y%2B1%29
Second term denominator:
y%5E2-1=%28y%2B1%29%28y-1%29
Multiply the first term by (y-1)/(y-1) and
then multiply the second term by (y+5)/(y+5) to get
the common denominator (y+1)(y-1)(y+5).
B:
B: %284y%5E2-4y-2y%5E2-10y%29%2F%28%28y%2B1%29%28y-1%29%28y%2B5%29%29
B: %282y%5E2-14y%29%2F%28%28y%2B1%29%28y-1%29%28y%2B5%29%29
B: 2y%28y-7%29%2F%28%28y%2B1%29%28y-1%29%28y%2B5%29%29