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\frac{x^{2}-1}{4x^{2}-x-3}
Combine x^{2} and 3x^{2} to get 4x^{2}.
\frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(4x+3\right)}
Factor the expressions that are not already factored.
\frac{x+1}{4x+3}
Cancel out x-1 in both numerator and denominator.
\frac{x^{2}-1}{4x^{2}-x-3}
Combine x^{2} and 3x^{2} to get 4x^{2}.
\frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(4x+3\right)}
Factor the expressions that are not already factored.
\frac{x+1}{4x+3}
Cancel out x-1 in both numerator and denominator.