SOLUTION: 3x+4overx+7 + x+2over2x+5 =1over2

Algebra ->  Inequalities -> SOLUTION: 3x+4overx+7 + x+2over2x+5 =1over2      Log On


   

Question 836395: 3x+4overx+7 + x+2over2x+5 =1over2
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2B4%29%2F%28x%2B7%29+%2B+%28x%2B2%29%2F%282x%2B5%29+=1%2F2
Develop common denominators


foil



%28+7x%5E2+%2B+32x+%2B+34+%29%2F%28+%28x+%2B+7%29%282x+%2B+5%29+%29+=+1%2F2+
%28+7x%5E2+%2B+32x+%2B+34+%29%2F%28+2x%5E2+%2B19x+%2B35+%29+=+1%2F2+
cross products
2%28+7x%5E2+%2B+32x+%2B+34+%29=1%28+2x%5E2+%2B19x+%2B35+%29++
14x%5E2+%2B+64x+%2B+68+=+2x%5E2+%2B19x+%2B35++
add -(2x^2 +19x +35) to each side
12x%5E2+%2B+45x+%2B+33+=+0++
The product of the outer coefficients is 396
Since 12 x 33 = 396 and 12+33 = 45 we can factor
12x%5E2+%2B+33x+%2B+12x%2B+33+=+0++
+3x%284x+%2B+11%29+%2B+3%284x+%2B+11%29+=+0++
+%283x+%2B+3%29%284x+%2B+11%29+=+0++
So either 3x + 3 = 0 or 4x + 11 = 0
Take 3x + 3 = 0
add -3 to each side
3x = -3
x = -1
Now 4x + 11 = 0
add -11 to each side
4x = -11
x = -11/4
Our solutions are x = -1 and x = -11/4