document.write( "Question 1101236: make x the subject of the formula
\n" ); document.write( "1. x/x+a - a/x+b = 1
\n" ); document.write( "2. x^2/a^2 + y^2/b^2 = 1
\n" ); document.write( "3. a(a^2- x) = b(b^2 - x)
\n" ); document.write( "4. a/a-x = b/b+x \n" ); document.write( "

Algebra.Com's Answer #715803 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
make x the subject of the formula
\n" ); document.write( " 1. $\"x%2F%28x%2Ba%29+-+a%2F%28x%2Bb%29+=+1\"$
\n" ); document.write( "multiply by (x+a)(x+b), cancel the denominators
\n" ); document.write( "x(x+b) - a(x+a) = (x+a)(x+b)
\n" ); document.write( "distribute, FOIL
\n" ); document.write( "x^2 + bx - ax - a^2 = x^2 + bx + ax + ab
\n" ); document.write( "combine like terms
\n" ); document.write( "x^2 - x^2 - ax - ax = a^2 + bx - bx + ab
\n" ); document.write( "-2ax = a^2 + ab
\n" ); document.write( " $\"x+=+%28a%5E2%2Bab%29%2F%28-2a%29\"$
\n" ); document.write( "factor out a
\n" ); document.write( " $\"x+=+%28a%28a%2Bb%29%29%2F%28-2a%29\"$
\n" ); document.write( "Cancel a
\n" ); document.write( " $\"x+=+-%28a%2Bb%29%2F2\"$
\n" ); document.write( ":
\n" ); document.write( " 2. $\"x%5E2%2Fa%5E2+%2B+y%5E2%2Fb%5E2+=+1\"$
\n" ); document.write( "multiply equation by a^2b^2
\n" ); document.write( " $\"b%5E2x%5E2+%2B+a%5E2y%5E2+=+a%5E2b%5E2\"$
\n" ); document.write( " $\"b%5E2x%5E2+=+a%5E2b%5E2+-+a%5E2y%5E2\"$
\n" ); document.write( " $\"b%5E2x%5E2+=+a%5E2%28b%5E2-y%5E2%29\"$
\n" ); document.write( " $\"x%5E2+=+%28a%5E2%28b%5E2-y%5E2%29%29%2Fb%5E2\"$
\n" ); document.write( " $\"x+=+sqrt%28%28a%5E2%28b%5E2-y%5E2%29%29%2Fb%5E2%29\"$
\n" ); document.write( "extract the squares
\n" ); document.write( " $\"x+=+%28a%2Fb%29sqrt%28b%5E2-y%5E2%29\"$
\n" ); document.write( ":
\n" ); document.write( "Will finish later today, these are time consuming.
\n" ); document.write( ":
\n" ); document.write( " 3. $\"a%28a%5E2-+x%29+=+b%28b%5E2+-+x%29\"$
\n" ); document.write( "a^3 - ax = b^3 - bx
\n" ); document.write( "bx - ax = b^3 - a^3
\n" ); document.write( "x(b-a) = b^3 - a^3
\n" ); document.write( "x = $\"%28b%5E3-a%5E3%29%2F%28b-a%29\"$
\n" ); document.write( ":
\n" ); document.write( " 4. $\"a%2F%28a-x%29+=+b%2F%28b%2Bx%29\"$
\n" ); document.write( "cross multiply
\n" ); document.write( "a(b+x) = b(a-x)
\n" ); document.write( "ab + ax = ab - bx
\n" ); document.write( "bx + ax = ab - ab
\n" ); document.write( "bx + ax = 0
\n" ); document.write( "x(b + a) = 0
\n" ); document.write( "x = $\"0%2F%28%28b%2Ba%29%29\"$
\n" ); document.write( "x = 0 \n" ); document.write( "

\n" );