document.write( "Question 21944: t+10 / 7-t = 3 / t-7 \n" ); document.write( "

Algebra.Com's Answer #10581 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
first cross-multiply (multiply both sides by 7-t, then multiply both sides by t-7)
\n" ); document.write( "(t + 10)(t - 7) = 3(7 - t)
\n" ); document.write( "t^2 + 3t - 70 = 3(7 - t)
\n" ); document.write( "expanding
\n" ); document.write( "t^2 + 3t - 70 = 21 - 3t
\n" ); document.write( "expanding
\n" ); document.write( "t^2 +6t -91 = 0
\n" ); document.write( "adding 3t to both sides and subtracting 21 from both sides
\n" ); document.write( "use the quadratic formula:
\n" ); document.write( " $\"%28-b+%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a\"$
\n" ); document.write( "you will get:
\n" ); document.write( " $\"%28-6+%2B-sqrt%2836+-+4%2A%28-91%29%29%29%2F2%29\"$
\n" ); document.write( " $\"%28-6+%2B-+20%29+%2F2\"$
\n" ); document.write( " $\"-3+%2B-+10\"$
\n" ); document.write( "7, -13
\n" ); document.write( "if you substitute 7 into the original equation, you get 7 - 7 in both denominators. this says infinity = infinity.
\n" ); document.write( "if you substitute -13 into the original equation, you get:
\n" ); document.write( " $\"%28-3%29+%2F+20+=+3+%2F+%28-20%29\"$
\n" ); document.write( "the solutions check ok \n" ); document.write( "

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