SOLUTION: {{{ (t^2-1)/(t^2-4) }}} + {{{ (9t+9)/(4t+12) }}} * {{{ (2-t)/(t^2+2t-3) }}} The back of the book lists the answer as {{{ -4/9(t/2) }}} written as -4 over 9(t÷2). I am havin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{ (t^2-1)/(t^2-4) }}} + {{{ (9t+9)/(4t+12) }}} * {{{ (2-t)/(t^2+2t-3) }}} The back of the book lists the answer as {{{ -4/9(t/2) }}} written as -4 over 9(t÷2). I am havin      Log On


   

Question 1144161: +%28t%5E2-1%29%2F%28t%5E2-4%29+ + +%289t%2B9%29%2F%284t%2B12%29+ * +%282-t%29%2F%28t%5E2%2B2t-3%29+
The back of the book lists the answer as +-4%2F9%28t%2F2%29+ written as -4 over 9(t÷2).
I am having trouble working through the problem. Although the answer is given, I would like to see how the problem is solved.
I started by factoring and multiplying +%289t%2B9%29%2F%284t%2B12%29+ * +%282-t%29%2F%28t%5E2%2B2t-3%29+
I got +%289%28t%2B1%29%29%2F%284%28t%2B3%29%29+ * +-%28t-2%29%2F%28t-1%29%28t%2B3%29+ which equals +-9%28t%2B1%29%28t-2%29%2F4%28t%2B3%29%5E2%28t-1%29+
Then I tried to add +%28t%5E2-1%29%2F%28t%5E2-4%29+ + -9%28t%2B1%29%28t-2%29%2F4%28t%2B3%29%5E2%28t-1%29+
I got an LCD of +4%28t%5E2-4%29%28t%2B3%29%5E2%28t-1%29+ OR +4%28t%2B2%29%28t-2%29%28t%2B3%29%28t%2B3%29%28t-1%29+ And that is where things get messy.
Found 3 solutions by Alan3354, greenestamps, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+%28t%5E2-1%29%2F%28t%5E2-4%29+ + %289t%2B9%29%2F%284t%2B12%29*%282-t%29%2F%28t%5E2%2B2t-3%29
= +%28t%5E2-1%29%2F%28t%5E2-4%29+ + 9%2A%28t%2B1%29%2F%284%2A%28t%2B3%29%29*%282-t%29%2F%28%28t%2B3%29%2A%28t-1%29%29
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If you sub t = 5, you find that the book's answer is wrong.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The answer you show from the book doesn't make any sense.
(1) The answer you show is an unsimplified rational expression; it could never be the final simplified answer to a problem.
(2) With all those binomials in all the rational expressions in the original problem, you aren't going to end up with a monomial answer.

It looks as if you are doing the right things, for the problem as you show it.

Are you sure you have shown the problem correctly? It might simplify considerably if the addition between the first two expressions were a multiplication instead....

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
+%28t%5E2-1%29%2F%28t%5E2-4%29+ + +%289t%2B9%29%2F%284t%2B12%29+ * +%282-t%29%2F%28t%5E2%2B2t-3%29+
The back of the book lists the answer as +-4%2F9%28t%2F2%29+ written as -4 over 9(t÷2).
I am having trouble working through the problem. Although the answer is given, I would like to see how the problem is solved.
I started by factoring and multiplying +%289t%2B9%29%2F%284t%2B12%29+ * +%282-t%29%2F%28t%5E2%2B2t-3%29+
I got +%289%28t%2B1%29%29%2F%284%28t%2B3%29%29+ * +-%28t-2%29%2F%28t-1%29%28t%2B3%29+ which equals +-9%28t%2B1%29%28t-2%29%2F4%28t%2B3%29%5E2%28t-1%29+
Then I tried to add +%28t%5E2-1%29%2F%28t%5E2-4%29+ + -9%28t%2B1%29%28t-2%29%2F4%28t%2B3%29%5E2%28t-1%29+
I got an LCD of +4%28t%5E2-4%29%28t%2B3%29%5E2%28t-1%29+ OR +4%28t%2B2%29%28t-2%29%28t%2B3%29%28t%2B3%29%28t-1%29+ And that is where things get messy.
In order to get anything close to the book's answer, I'd say that it's -+4%2F9%28t+%2B+2%29, and not -+4%2F9%28t%2F2%29

I do believe that %28t%5E2+-+1%29%2F%28t%5E2+-+4%29 + %289t+%2B+9%29%2F%284t+%2B+12%29 * %282+-+t%29%2F%28t%5E2+%2B+2t+-+3%29 should be %28t%5E2+-+1%29%2F%28t%5E2+-+4%29 ÷ +%289t%2B9%29%2F%284t%2B12%29+ * +%282-t%29%2F%28t%5E2%2B2t-3%29+, with a "÷" instead of a "+".

You should notice that this MUST be since for the answer the "4" and "9" changed positions from numerator to denominator, and vice-versa.

Look over the problem again! I believe you had a "+" instead of a "÷" in the expression, and a "÷" in the answer instead of a "+".

If that is so, then I do believe that you'll be able to get the correct answer. If not, I'd be glad to show you how to arrive at it.