Evaluate
-\frac{1}{3x-4y}
Expand
-\frac{4}{12x-16y}
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\frac{\left(12a-15a^{2}\right)\left(4y-4xy-3x^{2}+3x\right)}{\left(9x^{2}-16y^{2}\right)\left(3a-3ax\right)\left(5a-4\right)}
Divide \frac{12a-15a^{2}}{9x^{2}-16y^{2}} by \frac{\left(3a-3ax\right)\left(5a-4\right)}{4y-4xy-3x^{2}+3x} by multiplying \frac{12a-15a^{2}}{9x^{2}-16y^{2}} by the reciprocal of \frac{\left(3a-3ax\right)\left(5a-4\right)}{4y-4xy-3x^{2}+3x}.
\frac{3a\left(-5a+4\right)\left(-x+1\right)\left(3x+4y\right)}{3a\left(5a-4\right)\left(-x+1\right)\left(3x-4y\right)\left(3x+4y\right)}
Factor the expressions that are not already factored.
\frac{-3a\left(5a-4\right)\left(-x+1\right)\left(3x+4y\right)}{3a\left(5a-4\right)\left(-x+1\right)\left(3x-4y\right)\left(3x+4y\right)}
Extract the negative sign in 4-5a.
\frac{-1}{3x-4y}
Cancel out 3a\left(5a-4\right)\left(-x+1\right)\left(3x+4y\right) in both numerator and denominator.
\frac{\left(12a-15a^{2}\right)\left(4y-4xy-3x^{2}+3x\right)}{\left(9x^{2}-16y^{2}\right)\left(3a-3ax\right)\left(5a-4\right)}
Divide \frac{12a-15a^{2}}{9x^{2}-16y^{2}} by \frac{\left(3a-3ax\right)\left(5a-4\right)}{4y-4xy-3x^{2}+3x} by multiplying \frac{12a-15a^{2}}{9x^{2}-16y^{2}} by the reciprocal of \frac{\left(3a-3ax\right)\left(5a-4\right)}{4y-4xy-3x^{2}+3x}.
\frac{3a\left(-5a+4\right)\left(-x+1\right)\left(3x+4y\right)}{3a\left(5a-4\right)\left(-x+1\right)\left(3x-4y\right)\left(3x+4y\right)}
Factor the expressions that are not already factored.
\frac{-3a\left(5a-4\right)\left(-x+1\right)\left(3x+4y\right)}{3a\left(5a-4\right)\left(-x+1\right)\left(3x-4y\right)\left(3x+4y\right)}
Extract the negative sign in 4-5a.
\frac{-1}{3x-4y}
Cancel out 3a\left(5a-4\right)\left(-x+1\right)\left(3x+4y\right) in both numerator and denominator.
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