SOLUTION: I am having trouble with solving for x in the following equation: {{{ (x+1)/(x-3)=x+2 }}} So far I have tried the following steps to simplify: x+1=(x+2)(x-3) x+1={{{x^2-3

Algebra ->  Equations -> SOLUTION: I am having trouble with solving for x in the following equation: {{{ (x+1)/(x-3)=x+2 }}} So far I have tried the following steps to simplify: x+1=(x+2)(x-3) x+1={{{x^2-3      Log On


   

Question 456094: I am having trouble with solving for x in the following equation:
+%28x%2B1%29%2F%28x-3%29=x%2B2+
So far I have tried the following steps to simplify:
x+1=(x+2)(x-3)
x+1=x%5E2-3x%2B2x-6
x+1=x%5E2-x-6
x+7=x%5E2-x
2x+7=x%5E2
2+7=x%5E2%2Fx
9=x%5E2%2Fx
9x=x%5E2
9=x
However, when I plug this solution for x into a calculator I end up with %289%2B1%29%2F%289-3%29=+5%2F3, which is not = to 9+2.
I hope you can explain this to me! I've been trying for hours over the past couple of days and I'm just not understanding it.
Thank you for taking the time to read this.
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x+1)/(x-3)=x+2 }}}
So far I have tried the following steps to simplify:
x+1=(x+2)(x-3)
x+1=x%5E2-3x%2B2x-6
x+1=x%5E2-x-6
x+7=x%5E2-x
2x+7=x%5E2
----
Good up to this point:
Then:
x^2-2x-7 = 0
Now use the quadratic formula to solve for "x":
x = [2 +- sqrt(4-4*-7)]/2
----
x = [2 +- sqrt(32)]/2
---
x = [2 +- 4sqrt(2)]/2
---
x = 1+2sqrt(2) or x = 1 - 2sqrt(2)
==========================================
Cheers,
Stan H.
===============

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(x+1)/(x-3)=x+2
x+1=(x-3)(x+2)
x+1=x^2-x-6
x^2-2x-7=0
x=1-2sqrt(2), x=1+2sqrt(2) see below
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-7+=+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=%28-2%29%5E2-4%2A1%2A-7=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+3.82842712474619
x%5B2%5D+=+%28-%28-2%29-sqrt%28+32+%29%29%2F2%5C1+=+-1.82842712474619

Quadratic expression 1x%5E2%2B-2x%2B-7 can be factored:
1x%5E2%2B-2x%2B-7+=+1%28x-3.82842712474619%29%2A%28x--1.82842712474619%29
Again, the answer is: 3.82842712474619, -1.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-7+%29