SOLUTION: hello will someone please help me with this question (x-1)/(x+2)=(2x-3)/(x+4)

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Question 785009: hello will someone please help me with this question (x-1)/(x+2)=(2x-3)/(x+4)
Found 3 solutions by stanbon, edjones, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1)/(x+2)=(2x-3)/(x+4)
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Cross-multiply:::
(x+4)(x-1) = (x+2)(2x-3)
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x^2 + 3x -4 = 2x^2 +x -6
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x^2 -2x -2 = 0
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x = [2 +- sqrt(4-4*-2)]/2
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x = [2 +- sqrt(12)]/2
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x = [2 +- 2sqrt(3)]/2
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x = 1 +- sqrt(3)
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Cheers,
Stan H.
========================

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1)/(x+2)=(2x-3)/(x+4)
(x-1)(x+4)=(2x-3)(x+2)
x^2+3x-4=2x^2+x-6
x^2-2x-2=0
x=1+sqrt(3), x=1-sqrt(3) (see below)
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-2+=+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-2=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+2.73205080756888
x%5B2%5D+=+%28-%28-2%29-sqrt%28+12+%29%29%2F2%5C1+=+-0.732050807568877

Quadratic expression 1x%5E2%2B-2x%2B-2 can be factored:
1x%5E2%2B-2x%2B-2+=+%28x-2.73205080756888%29%2A%28x--0.732050807568877%29
Again, the answer is: 2.73205080756888, -0.732050807568877. 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-2+%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-1%29%2F%28x%2B2%29=%282x-3%29%2F%28x%2B4%29

cross multiply
(x-1)(x+4)=(2x-3)(x+2)


x%28x%2B4%29-1%28x%2B4%29=2x%28x%2B2%29-3%28x%2B2%29

x%5E2%2B4x-x-4=2x%5E2%2B4x-3x-6
re arrange
2x%5E2-x%5E2%2B4x-3x-4x%2Bx=-4%2B6
x%5E2-2x-2=0

x%5E2-2x%2B1=+2%2B1
%28x%2B1%29%5E2=3
x+1 = +/- sqrt(3)
x= 1+sqrt(3) OR 1-sqrt(3)

m.ananth@hotmail.ca