Evaluate
\frac{x-1}{x+4}
Expand
\frac{x-1}{x+4}
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\frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)}-\frac{2x}{x+1}+\frac{13}{x+4}
Factor x^{2}+5x+4.
\frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)}-\frac{2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x+4\right) and x+1 is \left(x+1\right)\left(x+4\right). Multiply \frac{2x}{x+1} times \frac{x+4}{x+4}.
\frac{3x^{2}-5x-14-2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Since \frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)} and \frac{2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-5x-14-2x^{2}-8x}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Do the multiplications in 3x^{2}-5x-14-2x\left(x+4\right).
\frac{x^{2}-13x-14}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Combine like terms in 3x^{2}-5x-14-2x^{2}-8x.
\frac{\left(x-14\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Factor the expressions that are not already factored in \frac{x^{2}-13x-14}{\left(x+1\right)\left(x+4\right)}.
\frac{x-14}{x+4}+\frac{13}{x+4}
Cancel out x+1 in both numerator and denominator.
\frac{x-14+13}{x+4}
Since \frac{x-14}{x+4} and \frac{13}{x+4} have the same denominator, add them by adding their numerators.
\frac{x-1}{x+4}
Combine like terms in x-14+13.
\frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)}-\frac{2x}{x+1}+\frac{13}{x+4}
Factor x^{2}+5x+4.
\frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)}-\frac{2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+1\right)\left(x+4\right) and x+1 is \left(x+1\right)\left(x+4\right). Multiply \frac{2x}{x+1} times \frac{x+4}{x+4}.
\frac{3x^{2}-5x-14-2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Since \frac{3x^{2}-5x-14}{\left(x+1\right)\left(x+4\right)} and \frac{2x\left(x+4\right)}{\left(x+1\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-5x-14-2x^{2}-8x}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Do the multiplications in 3x^{2}-5x-14-2x\left(x+4\right).
\frac{x^{2}-13x-14}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Combine like terms in 3x^{2}-5x-14-2x^{2}-8x.
\frac{\left(x-14\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}+\frac{13}{x+4}
Factor the expressions that are not already factored in \frac{x^{2}-13x-14}{\left(x+1\right)\left(x+4\right)}.
\frac{x-14}{x+4}+\frac{13}{x+4}
Cancel out x+1 in both numerator and denominator.
\frac{x-14+13}{x+4}
Since \frac{x-14}{x+4} and \frac{13}{x+4} have the same denominator, add them by adding their numerators.
\frac{x-1}{x+4}
Combine like terms in x-14+13.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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
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