SOLUTION: Solve each of the following equations for x. 5 over x + 6 PLUS 2 over x squared + 7x + 6 EQUALS 3 over x + 1 2 over 5 = x - 2 over 20

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve each of the following equations for x. 5 over x + 6 PLUS 2 over x squared + 7x + 6 EQUALS 3 over x + 1 2 over 5 = x - 2 over 20      Log On


   

Question 116813: Solve each of the following equations for x.
5 over x + 6 PLUS 2 over x squared + 7x + 6 EQUALS 3 over x + 1

2 over 5 = x - 2 over 20
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each of the following equations for+x:


1.

5%2F%28x%2B6%29+%2B+2%2F%28x%5E2+%2B+7x+%2B+6%29+=+3%2F%28x%2B1%29………. replace 7x+ with x%2B6x

5%2F%28x%2B6%29+%2B+2%2F%28x%5E2+%2B+x+%2B+6x+%2B+6%29+=+3%2F%28x%2B1%29………. group the first two terms together and the last two terms together
5%2F%28x%2B6%29+%2B+2%2F%28%28x%5E2+%2B+x+%29%2B+%286x+%2B+6%29%29+=+3%2F%28x%2B1%29………. factor a x out of the first group and factor a 6 out of the second group
5%2F%28x%2B6%29+%2B+2%2F%28x%28x+%2B+1+%29%2B+6%28x+%2B+1%29%29+=+3%2F%28x%2B1%29………. combine like terms
5%2F%28x%2B6%29+%2B+2%2F%28%28x+%2B+6%29%28x+%2B+1%29%29+=+3%2F%28x%2B1%29……….common denominator is +%28x+%2B+6%29%28x+%2B+1%29; multiply both sides by it
……….cancel out
5%28x+%2B+1%29+%2B+2=+3+%28x+%2B+6%29……….
5x+%2B+5+%2B+2=+3+x+%2B+18……….
5x+-3x=+18+%96+5+-+2……….
2x=+11……….

x=+11%2F2……….
x=+5.5……….

check:
5%2F%28x%2B6%29+%2B+2%2F%28x%5E2+%2B+7x+%2B+6%29+=+3%2F%28x%2B1%29……….
5%2F%285.5%2B6%29+%2B+2%2F%28%285.5%29%5E2+%2B+7%2A5.5+%2B+6%29+=+3%2F%285.5%2B1%29……….
5%2F11.5+%2B+2%2F%2830.25+%2B+38.5+%2B+6%29+=+3%2F6.5……….
0.43+%2B+2%2F74.75+=+0.46……….
0.43+%2B+0.02675=+0.46……….
0.456+=+0.46……….
0.46+=+0.46……….




2.
2%2F5+=+%28x-2%29%2F20………. multiply both sides by 20
20%2A2%2F5+=+20%28x-2%29%2F20……….

4%2A2+=+%28x-2%29……….
8+%2B2=x+
x+=+10++
check
2%2F5+=+%28x-2%29%2F20……….
2%2F5+=+%2810-2%29%2F20……….
2%2F5+=+8%2F20………. reduce 8%2F20=%288%3A4%29%2F%2820%3A4%29
2+%2F+5+=+2%2F+5………….