SOLUTION: Please help me solve this equation and check my solution. {{{ 18/(x-3) = x/3 }}} Sorry I didn't know how to put the line under the numerator!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this equation and check my solution. {{{ 18/(x-3) = x/3 }}} Sorry I didn't know how to put the line under the numerator!!!       Log On


   

Question 75030This question is from textbook
: Please help me solve this equation and check my solution. +18%2F%28x-3%29+=+x%2F3+
Sorry I didn't know how to put the line under the numerator!!! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To make a fraction of 18%2F%28x-3%29 just place 18/(x-3) in triple curly brackets.
+18%2F%28x-3%29+=+x%2F3+ Start with the given problem
+%283%2F1%29%2818%2F%28x-3%29%29+=+%28x%2Fcross%283%29%29%28cross%283%29%2F1%29Multiply both sides by 3, this eliminates the denominator of the right side
cross%28x-3%29%2854%2Fcross%28x-3%29%29=x%28x-3%29Multiply both sides by (x-3), this eliminates the denominator of the left side
So we're left with this:
54=x%28x-3%29
54=x%5E2-3x%29Distribute the x
0=x%5E2-3x-54%29Subtract 54 from both sides
0=%28x-9%29%28x%2B6%29Factor the right side
x-9=0
x=9There's one answer
x%2B6=0
x=-6There's the other answer
So the solution is x=9 and x=-6


Check:
+18%2F%28x-3%29+=+x%2F3+Plug in x=9
+18%2F%289-3%29+=+9%2F3+
+18%2F6+=+3+
+3=+3+works
+18%2F%28x-3%29+=+x%2F3+Plug in x=-6
+18%2F%28%28-6%29-3%29+=+-6%2F3+
+18%2F%28-9%29+=+-2+
+-2=+-2+works
Here's another way to solve it:
When you have the quadratic 0=x%5E2-3x-54%29, plug the coefficients into the quadratic formula:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-54+=+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=%28-3%29%5E2-4%2A1%2A-54=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-3%29-sqrt%28+225+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B-3x%2B-54 can be factored:
1x%5E2%2B-3x%2B-54+=+1%28x-9%29%2A%28x--6%29
Again, the answer is: 9, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-54+%29

And you see the same answer, but it's just another way to get there.