SOLUTION: Please help me solve sqrt( 2x - 1 ) - sqrt( x - 1 ) = 1

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Question 1133262: Please help me solve sqrt( 2x - 1 ) - sqrt( x - 1 ) = 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%282x+-+1%29+-+sqrt%28x+-+1%29+=+1+

sqrt%282x+-+1%29+=+1%2Bsqrt%28+x+-+1+%29+........square both sides

%28sqrt%282x+-+1%29%29%5E2+=+%281%2Bsqrt%28+x+-+1+%29%29%5E2+
2x+-+1+=+1%2B2sqrt%28+x+-+1+%29%2B%28sqrt%28+x+-+1+%29%29%5E2
2x+-+1+=+cross%281%29%2B2sqrt%28+x+-+1+%29%2B+x+-+cross%281%29
2x+-+1+=+2sqrt%28+x+-+1+%29%2B+x+
2x+-+1-x+=+2sqrt%28+x+-+1+%29+
x+-+1+=+2sqrt%28+x+-+1+%29+.....square both sides

%28x+-+1%29%5E2=+%282%2Asqrt%28+x+-+1+%29%29%5E2++
x%5E2+-+2x%2B1=4%28+x+-+1+%29++
x%5E2+-+2x%2B1=4x+-+4+
x%5E2+-+2x%2B1-4x+%2B4=0+
x%5E2+-+6x%2B5=0+
x%5E2+-+x-5x%2B5=0+
%28x%5E2+-+x%29-%285x-5%29=0+
x%28x+-+1%29-5%28x-1%29=0+
%28x+-+1%29+%28+x+-+5%29+=+0

solutions:
if %28x+-+1%29+=+0=>x=1
if %28+x+-5%29+=+0=>x=5