document.write( "Question 950246: solve for all values of x: x-1/x-5 - 1/5= 20/x^2-5x \n" ); document.write( "

Algebra.Com's Answer #580382 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Assume the equation is:
\n" ); document.write( " $\"%28%28x-1%29%29%2F%28%28x-5%29%29+-+1%2F5+=+20%2F%28%28x%5E2-5x%29%29\"$
\n" ); document.write( "Factor out x
\n" ); document.write( " $\"%28%28x-1%29%29%2F%28%28x-5%29%29+-+1%2F5+=+20%2F%28x%28x-5%29%29\"$
\n" ); document.write( "multiply by the common denominator 5x(x-5)
\n" ); document.write( "5x(x-5)* $\"%28%28x-1%29%29%2F%28%28x-5%29%29\"$ - 5x(x-5)* $\"1%2F5\"$ = 5x(x-5)* $\"20%2F%28x%28x-5%29%29\"$
\n" ); document.write( "cancel the denomonators
\n" ); document.write( "5x(x-1) - x(x-5) = 5(20)
\n" ); document.write( "5x^2 - 5x - x^2 + 5x = 100
\n" ); document.write( "Combine like terms
\n" ); document.write( "5x^2 - x^2 - 5x + 5x = 100
\n" ); document.write( "4x^2 = 100
\n" ); document.write( "x^2 = 100/4
\n" ); document.write( "x^2 = 25
\n" ); document.write( "x = +/- $\"sqrt%2825%29\"$
\n" ); document.write( "x = 5
\n" ); document.write( "or
\n" ); document.write( "x =-5
\n" ); document.write( ":
\n" ); document.write( "x = 5 cannot be a solution, we would have division by 0 in the original problem
\n" ); document.write( "however
\n" ); document.write( "x = -5 seems to work ok in the original problem, only solution \n" ); document.write( "

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