Add or subtract. Then simplify. If a denominator has three or more facotrs (Other then monomials.) Leave it in factored form.

Question

Add or subtract. Then simplify. If a denominator has three or more facotrs (Other then monomials.) Leave it in factored form.

 

3y+2/y^2+5y-24  + 7/y^2+4y-32

Answer 1

Factoring y² + 5y - 24, you have (y + 8)(y - 3).  Factoring the y² + 4y - 32, you end up with factors of (y + 8)(y - 4).  The common denominator will be (y + 8)(y - 3)(y - 4).  When adding both sides of the equation, you end up with (3y + 2)(y - 4) + 7(y - 3) all over the common denom.  The first pair of numerators yield 3y² + 2y - 12y - 8 plus the right side of (7y - 21).  Adding like terms, you end up with 3y² - 3y - 29 for you answer.  To check the answer, let y = 2.  Substitute that value of y into the left side: 3 (2) + 2 = 8.  Now the denom. would be 2² + 5(2) - 24.  That comes to -10.  In the second part of the equation, the numerator is 7 and the denom. is 2² +4(2) - 32, which equals -20.  So, now were are at -8/10 - 7/20.  Use common denom. of 20, and you now have 2(-8) - 1(7) = -16 - 7 = -23.  Now substitute the y=2 into your answer of 3y² - 3y - 29 and you end up with 3(2)² -3(2) -29.  Now that leaves you with 3(4)-6-29.  12 - 6 - 29 = -23.  Compare the two (-23)'s and you have proven that your answer is correct.  Good luck!!