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\frac{2x^{2}-15x+7}{x^{2}-3x-4}\times \frac{\left(x+3\right)\left(x+4\right)}{\left(2x-1\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{x^{2}+7x+12}{2x^{2}+5x-3}.
\frac{2x^{2}-15x+7}{x^{2}-3x-4}\times \frac{x+4}{2x-1}
Cancel out x+3 in both numerator and denominator.
\frac{\left(2x^{2}-15x+7\right)\left(x+4\right)}{\left(x^{2}-3x-4\right)\left(2x-1\right)}
Multiply \frac{2x^{2}-15x+7}{x^{2}-3x-4} times \frac{x+4}{2x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-7\right)\left(2x-1\right)\left(x+4\right)}{\left(x-4\right)\left(2x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(x-7\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Cancel out 2x-1 in both numerator and denominator.
\frac{x^{2}-3x-28}{x^{2}-3x-4}
Expand the expression.
\frac{2x^{2}-15x+7}{x^{2}-3x-4}\times \frac{\left(x+3\right)\left(x+4\right)}{\left(2x-1\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{x^{2}+7x+12}{2x^{2}+5x-3}.
\frac{2x^{2}-15x+7}{x^{2}-3x-4}\times \frac{x+4}{2x-1}
Cancel out x+3 in both numerator and denominator.
\frac{\left(2x^{2}-15x+7\right)\left(x+4\right)}{\left(x^{2}-3x-4\right)\left(2x-1\right)}
Multiply \frac{2x^{2}-15x+7}{x^{2}-3x-4} times \frac{x+4}{2x-1} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-7\right)\left(2x-1\right)\left(x+4\right)}{\left(x-4\right)\left(2x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored.
\frac{\left(x-7\right)\left(x+4\right)}{\left(x-4\right)\left(x+1\right)}
Cancel out 2x-1 in both numerator and denominator.
\frac{x^{2}-3x-28}{x^{2}-3x-4}
Expand the expression.