SOLUTION: The problem that I am working on is this one: 1/a-b + 4/b-a -8/a+b - 11a-5b/b^2-a^2 I know that I have to find the common denominator but on this problem I keep getting confused..

Algebra ->  Equations -> SOLUTION: The problem that I am working on is this one: 1/a-b + 4/b-a -8/a+b - 11a-5b/b^2-a^2 I know that I have to find the common denominator but on this problem I keep getting confused..      Log On


   



Question 454769: The problem that I am working on is this one:
1/a-b + 4/b-a -8/a+b - 11a-5b/b^2-a^2 I know that I have to find the common denominator but on this problem I keep getting confused...

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F%28a-b%29+%2B+4%2F%28b-a%29+-+8%2F%28a%2Bb%29+-+%2811a-5b%29+%2F+%28b%5E2-a%5E2%29+
First factor the denominator of the last term

Now express the first term as: +1%2F%28a+-+b%29+=+-1%2F%28b+-+a%29+

Combine the first two terms:
++-1%2F%28b+-+a%29+%2B+4%2F%28b-a%29+=+%284+-+1%29+%2F+%28b+-+a%29+
+%284+-+1%29+%2F+%28b+-+a%29+=+3+%2F+%28b-a%29+
So far I have:
+3+%2F+%28b-a%29+-+8%2F%28b+%2B+a%29+-+%2811a-5b%29+%2F+%28%28b+-+a%29%2A%28+b+%2B+a%29%29+
Now multiply top and bottom of 1st term by +%28b+%2B+a%29+%2F+%28b+%2B+a%29+
Multiply top and bottom of 2nd term by +%28b+-+a%29%2A%28b+-+a%29+

Now combine the fractions with common denominator:

Combine terms in the numerator
+%28+3b+%2B+3a+-+8b+%2B+8a+-+11a+%2B+5b%29+%2F+%28%28b+-+a%29%2A%28b+%2B+a%29%29+
+%28+3a+%2B+8a+-+11a+%2B+3b+-+8b+%2B+5b+%29+%2F+%28%28b+-+a%29%2A%28b+%2B+a%29%29+
The numerator is +0+, so
+1%2F%28a-b%29+%2B+4%2F%28b-a%29+-+8%2F%28a%2Bb%29+-+%2811a-5b%29+%2F+%28b%5E2-a%5E2%29+=+0+
One way to check the answer is to give values for a and b
Note that a cannot = b, since the answer would be +0%2F0+
I'll say +a+=+3, +b+=+5+
+1%2F%28a-b%29+%2B+4%2F%28b-a%29+-+8%2F%28a%2Bb%29+-+%2811a-5b%29+%2F+%28b%5E2-a%5E2%29+=+0+

+1%2F%28-2%29+%2B+4%2F+2+-+8%2F8+-+%2833+-+25%29+%2F+%2825+-+9%29+=+0+
+-1%2F2+%2B+4%2F+2+-+2%2F2+-+8+%2F+16+=+0+
+1%2F2+-+1%2F2+=+0+
+0+=+0+
OK