Evaluate
\frac{2x+3}{x+3}
Expand
\frac{2x+3}{x+3}
Graph
Share
Copied to clipboard
\frac{\frac{x^{2}}{\left(x-3\right)\left(x+3\right)}-\frac{x+1}{x+3}}{\frac{1}{x-3}}
Factor x^{2}-9.
\frac{\frac{x^{2}}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{x+1}{x+3} times \frac{x-3}{x-3}.
\frac{\frac{x^{2}-\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Since \frac{x^{2}}{\left(x-3\right)\left(x+3\right)} and \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{2}-x^{2}+3x-x+3}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Do the multiplications in x^{2}-\left(x+1\right)\left(x-3\right).
\frac{\frac{2x+3}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Combine like terms in x^{2}-x^{2}+3x-x+3.
\frac{\left(2x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}
Divide \frac{2x+3}{\left(x-3\right)\left(x+3\right)} by \frac{1}{x-3} by multiplying \frac{2x+3}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{1}{x-3}.
\frac{2x+3}{x+3}
Cancel out x-3 in both numerator and denominator.
\frac{\frac{x^{2}}{\left(x-3\right)\left(x+3\right)}-\frac{x+1}{x+3}}{\frac{1}{x-3}}
Factor x^{2}-9.
\frac{\frac{x^{2}}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x+3 is \left(x-3\right)\left(x+3\right). Multiply \frac{x+1}{x+3} times \frac{x-3}{x-3}.
\frac{\frac{x^{2}-\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Since \frac{x^{2}}{\left(x-3\right)\left(x+3\right)} and \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x^{2}-x^{2}+3x-x+3}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Do the multiplications in x^{2}-\left(x+1\right)\left(x-3\right).
\frac{\frac{2x+3}{\left(x-3\right)\left(x+3\right)}}{\frac{1}{x-3}}
Combine like terms in x^{2}-x^{2}+3x-x+3.
\frac{\left(2x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}
Divide \frac{2x+3}{\left(x-3\right)\left(x+3\right)} by \frac{1}{x-3} by multiplying \frac{2x+3}{\left(x-3\right)\left(x+3\right)} by the reciprocal of \frac{1}{x-3}.
\frac{2x+3}{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}