SOLUTION: hello I am having a hard time solving this equation, and would appreciate it if you would help me solve this problem: 1 1 1 - + - = - x x+3 4 I tried to rear

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: hello I am having a hard time solving this equation, and would appreciate it if you would help me solve this problem: 1 1 1 - + - = - x x+3 4 I tried to rear      Log On


   

Question 526830: hello I am having a hard time solving this equation, and would appreciate it if you would help me solve this problem:
1 1 1
- + - = -
x x+3 4
I tried to rearrange numbers to eliminate fractions and got
and got 4 = 2x + 3
1 = 2x

1
- = x
2
I am really struggling solving quadratic problems involving fractions. Wondering if you may have any tips or suggestions. Thank you in advance. -Shae

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2F%28x%2B3%29+=+1%2F4
trick is to multiply both sides by a common denominator 4x(x+3) to rid ourselves of all the denominators:
.
Multiplying both sides by 4x(x+3) we get:
4%28x%2B3%29+%2B+4x+=+x%28x%2B3%29
4x%2B12+%2B+4x+=+x%5E2%2B3x
8x%2B12+=+x%5E2%2B3x
12+=+x%5E2-5x
0+=+x%5E2-5x-12
since we can't factor, we apply the quadratic formula to get:
x = {6.772, -1.772}
.
Details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-12+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A1%2A-12=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+73+%29%29%2F2%5C1+=+6.77200187265877
x%5B2%5D+=+%28-%28-5%29-sqrt%28+73+%29%29%2F2%5C1+=+-1.77200187265877

Quadratic expression 1x%5E2%2B-5x%2B-12 can be factored:
1x%5E2%2B-5x%2B-12+=+1%28x-6.77200187265877%29%2A%28x--1.77200187265877%29
Again, the answer is: 6.77200187265877, -1.77200187265877. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-12+%29