Evaluate
-\frac{1}{x+3}
Expand
-\frac{1}{x+3}
Graph
Share
Copied to clipboard
\frac{\frac{5}{x+2}-\frac{x+2}{x+2}}{\frac{x^{2}-9}{x+2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.
\frac{\frac{5-\left(x+2\right)}{x+2}}{\frac{x^{2}-9}{x+2}}
Since \frac{5}{x+2} and \frac{x+2}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{5-x-2}{x+2}}{\frac{x^{2}-9}{x+2}}
Do the multiplications in 5-\left(x+2\right).
\frac{\frac{3-x}{x+2}}{\frac{x^{2}-9}{x+2}}
Combine like terms in 5-x-2.
\frac{\left(3-x\right)\left(x+2\right)}{\left(x+2\right)\left(x^{2}-9\right)}
Divide \frac{3-x}{x+2} by \frac{x^{2}-9}{x+2} by multiplying \frac{3-x}{x+2} by the reciprocal of \frac{x^{2}-9}{x+2}.
\frac{-x+3}{x^{2}-9}
Cancel out x+2 in both numerator and denominator.
\frac{-x+3}{\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{-\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}
Extract the negative sign in 3-x.
\frac{-1}{x+3}
Cancel out x-3 in both numerator and denominator.
\frac{\frac{5}{x+2}-\frac{x+2}{x+2}}{\frac{x^{2}-9}{x+2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.
\frac{\frac{5-\left(x+2\right)}{x+2}}{\frac{x^{2}-9}{x+2}}
Since \frac{5}{x+2} and \frac{x+2}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{5-x-2}{x+2}}{\frac{x^{2}-9}{x+2}}
Do the multiplications in 5-\left(x+2\right).
\frac{\frac{3-x}{x+2}}{\frac{x^{2}-9}{x+2}}
Combine like terms in 5-x-2.
\frac{\left(3-x\right)\left(x+2\right)}{\left(x+2\right)\left(x^{2}-9\right)}
Divide \frac{3-x}{x+2} by \frac{x^{2}-9}{x+2} by multiplying \frac{3-x}{x+2} by the reciprocal of \frac{x^{2}-9}{x+2}.
\frac{-x+3}{x^{2}-9}
Cancel out x+2 in both numerator and denominator.
\frac{-x+3}{\left(x-3\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{-\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}
Extract the negative sign in 3-x.
\frac{-1}{x+3}
Cancel out x-3 in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}