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\frac{x-3}{x-1}
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\frac{x-3}{x-1}
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\frac{x^{2}-2-\left(-4x+19\right)}{x^{2}+6x-7}
Since \frac{x^{2}-2}{x^{2}+6x-7} and \frac{-4x+19}{x^{2}+6x-7} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2+4x-19}{x^{2}+6x-7}
Do the multiplications in x^{2}-2-\left(-4x+19\right).
\frac{x^{2}-21+4x}{x^{2}+6x-7}
Combine like terms in x^{2}-2+4x-19.
\frac{\left(x-3\right)\left(x+7\right)}{\left(x-1\right)\left(x+7\right)}
Factor the expressions that are not already factored in \frac{x^{2}-21+4x}{x^{2}+6x-7}.
\frac{x-3}{x-1}
Cancel out x+7 in both numerator and denominator.
\frac{x^{2}-2-\left(-4x+19\right)}{x^{2}+6x-7}
Since \frac{x^{2}-2}{x^{2}+6x-7} and \frac{-4x+19}{x^{2}+6x-7} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2+4x-19}{x^{2}+6x-7}
Do the multiplications in x^{2}-2-\left(-4x+19\right).
\frac{x^{2}-21+4x}{x^{2}+6x-7}
Combine like terms in x^{2}-2+4x-19.
\frac{\left(x-3\right)\left(x+7\right)}{\left(x-1\right)\left(x+7\right)}
Factor the expressions that are not already factored in \frac{x^{2}-21+4x}{x^{2}+6x-7}.
\frac{x-3}{x-1}
Cancel out x+7 in both numerator and denominator.
Examples
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}