document.write( "Question 571082: How do I solve fractions like this: m+n over m-n minus m over m+n minus 2m squared over n squared - m squared ? \n" ); document.write( "

Algebra.Com's Answer #368025 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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How do I solve fractions like this: m+n over m-n minus m over m+n minus 2m squared over n squared - m squared ?
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\n" ); document.write( "You can't solve this, you have no equal sign, you can only simplify it.
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\n" ); document.write( "Assuming the problem is:
\n" ); document.write( " $\"%28m%2Bn%29%2F%28m-n%29\"$ - $\"m%2F%28m%2Bn%29\"$ - $\"%282m%5E2%29%2F%28n%5E2+-+m%5E2%29\"$
\n" ); document.write( "we want to change the signs in the third denominator so we can factor the difference of squares to:
\n" ); document.write( " $\"%28m%2Bn%29%2F%28m-n%29\"$ - $\"m%2F%28m%2Bn%29\"$ - $\"%282m%5E2%29%2F%28-1%28m%5E2-n%5E2%29%29\"$
\n" ); document.write( "that changes the sign to:
\n" ); document.write( " $\"%28m%2Bn%29%2F%28m-n%29\"$ - $\"m%2F%28m%2Bn%29\"$ + $\"%282m%5E2%29%2F%28%28m%5E2-n%5E2%29%29\"$
\n" ); document.write( "Factor
\n" ); document.write( " $\"%28m%2Bn%29%2F%28m-n%29\"$ - $\"m%2F%28m%2Bn%29\"$ + $\"%282m%5E2%29%2F%28%28m%2Bn%29%28m-n%29%29\"$
\n" ); document.write( "you can see we can put this over a single denominator
\n" ); document.write( " $\"%28%28m%2Bn%29%28m%2Bn%29+-+m%28m-n%29+%2B+2m%5E2%29%2F%28%28m%2Bm%29%28m-n%29%29\"$ = $\"%28m%5E2%2B2mn%2Bn%5E2+-+m%5E2%2Bmn+%2B+2m%5E2%29%2F%28%28m%2Bm%29%28m-n%29%29\"$
\n" ); document.write( "combine like terms, then factor
\n" ); document.write( " $\"%282m%5E2+%2B+3mn+%2B+n%5E2%29%2F%28%28m%2Bm%29%28m-n%29%29\"$ = $\"%28%282m%2Bn%29%28m%2Bn%29%29%2F%28%28m%2Bm%29%28m-n%29%29\"$
\n" ); document.write( "Cancel the (m+n), leaving us with
\n" ); document.write( " $\"%282m%2Bn%29%2F%28m-n%29\"$ \n" ); document.write( "

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