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\frac{7}{x+1}
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\frac{7}{x+1}
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\frac{4\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3x-3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{4x+8}{x^{2}+3x+2}.
\frac{4}{x+1}+\frac{3x-3}{x^{2}-1}
Cancel out x+2 in both numerator and denominator.
\frac{4}{x+1}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x-3}{x^{2}-1}.
\frac{4}{x+1}+\frac{3}{x+1}
Cancel out x-1 in both numerator and denominator.
\frac{7}{x+1}
Since \frac{4}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators. Add 4 and 3 to get 7.
\frac{4\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3x-3}{x^{2}-1}
Factor the expressions that are not already factored in \frac{4x+8}{x^{2}+3x+2}.
\frac{4}{x+1}+\frac{3x-3}{x^{2}-1}
Cancel out x+2 in both numerator and denominator.
\frac{4}{x+1}+\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}
Factor the expressions that are not already factored in \frac{3x-3}{x^{2}-1}.
\frac{4}{x+1}+\frac{3}{x+1}
Cancel out x-1 in both numerator and denominator.
\frac{7}{x+1}
Since \frac{4}{x+1} and \frac{3}{x+1} have the same denominator, add them by adding their numerators. Add 4 and 3 to get 7.
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}