SOLUTION: We were told to find ALL solutions real and imaginary and I'm really stuck on this problem: 6/x+8/(x+5)=3

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Question 764517: We were told to find ALL solutions real and imaginary and I'm really stuck on this problem:
6/x+8/(x+5)=3
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
6%2Fx%2B8%2F%28x%2B5%29=3....common denominator
6%2F%28x%28x%2B5%29%29%2B8%2F%28x%28x%2B5%29%29=3
%286%28x%2B5%29%2B8x%29%2F%28x%28x%2B5%29%29=3
6%28x%2B5%29%2B8x=3%28x%28x%2B5%29%29
6x%2B30%2B8x=3%28x%5E2%2B5x%29
14x%2B30=3x%5E2%2B15x
0=3x%5E2%2B15x-14x-30
3x%5E2%2Bx-30=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A3%2A%28-30%29+%29%29%2F%282%2A3%29+
x+=+%28-1+%2B-+sqrt%28+1%2B360+%29%29%2F6+
x+=+%28-1+%2B-+sqrt%28+361+%29%29%2F6+
x+=+%28-1+%2B-19%29%2F6+
solutions:
x+=+%28-1+%2B19%29%2F6+
x+=+18%2F6+
x+=+3
or
x+=+%28-1+-19%29%2F6+
x+=+-20%2F6+
x+=+-3.33
so, you have two real solutions:x+=+3 and x+=+-3.33


+graph%28+600%2C+600%2C+-10%2C+10%2C+-40%2C+10%2C+3x%5E2%2Bx-30%29+





Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+6%2Fx+%2B+8%2F%28x%2B5%29+=+3+
Multiply both sides by +x%2A%28+x%2B5+%29+
+6%2A%28+x%2B5+%29+%2B+8x+=+3x%2A%28+x%2B5+%29+
+6x+%2B+30+%2B+8x+=+3x%5E2+%2B+15x+
+14x+%2B+30+=+3x%5E2+%2B+15x+
+3x%5E2+%2B+x+-+30+=+0+
use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+1+
+c+=+-30+
+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A3%2A%28-30%29+%29%29+%2F+%282%2A3%29+
+x+=+%28-1+%2B-+sqrt%28+1+%2B+360+%29%29+%2F+6+
+x+=+%28-1+%2B-+sqrt%28+361+%29%29+%2F+6+
+x+=+%28-1+%2B+19+%29+%2F+6+
+x+=+18%2F6+
+x+=+3+
and, also
+x+=+%28-1+-+19+%29+%2F+6+
+x+=+-20%2F6+
+x+=+-10%2F3+
-------------
check:
+%28+x+-+3+%29%2A%28+x+%2B+10%2F3+%29+=+0+
+x%5E2+-+3x+%2B+%2810%2F3%29%2Ax+-+10+=+0+
+x%5E2+-+%289%2F3%29%2Ax+%2B+%2810%2F3%29%2Ax+-+10+=+0+
+x%5E2+%2B+%281%2F3%29%2Ax+-+10+=+0+
+3x%5E2+%2B+x+-+30+=+0+
OK