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\frac{x+1}{2x+3}
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\frac{x+1}{2x+3}
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\frac{2x+3}{\left(3x-2\right)\left(2x+3\right)}+\frac{x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-2 and 2x+3 is \left(3x-2\right)\left(2x+3\right). Multiply \frac{1}{3x-2} times \frac{2x+3}{2x+3}. Multiply \frac{x}{2x+3} times \frac{3x-2}{3x-2}.
\frac{2x+3+x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Since \frac{2x+3}{\left(3x-2\right)\left(2x+3\right)} and \frac{x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+3+3x^{2}-2x}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Do the multiplications in 2x+3+x\left(3x-2\right).
\frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Combine like terms in 2x+3+3x^{2}-2x.
\frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{\left(3x-2\right)\left(2x+3\right)}
Factor 6x^{2}+5x-6.
\frac{3+3x^{2}+x-5}{\left(3x-2\right)\left(2x+3\right)}
Since \frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)} and \frac{x-5}{\left(3x-2\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{-2+3x^{2}+x}{\left(3x-2\right)\left(2x+3\right)}
Combine like terms in 3+3x^{2}+x-5.
\frac{\left(3x-2\right)\left(x+1\right)}{\left(3x-2\right)\left(2x+3\right)}
Factor the expressions that are not already factored in \frac{-2+3x^{2}+x}{\left(3x-2\right)\left(2x+3\right)}.
\frac{x+1}{2x+3}
Cancel out 3x-2 in both numerator and denominator.
\frac{2x+3}{\left(3x-2\right)\left(2x+3\right)}+\frac{x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-2 and 2x+3 is \left(3x-2\right)\left(2x+3\right). Multiply \frac{1}{3x-2} times \frac{2x+3}{2x+3}. Multiply \frac{x}{2x+3} times \frac{3x-2}{3x-2}.
\frac{2x+3+x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Since \frac{2x+3}{\left(3x-2\right)\left(2x+3\right)} and \frac{x\left(3x-2\right)}{\left(3x-2\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{2x+3+3x^{2}-2x}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Do the multiplications in 2x+3+x\left(3x-2\right).
\frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{6x^{2}+5x-6}
Combine like terms in 2x+3+3x^{2}-2x.
\frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)}+\frac{x-5}{\left(3x-2\right)\left(2x+3\right)}
Factor 6x^{2}+5x-6.
\frac{3+3x^{2}+x-5}{\left(3x-2\right)\left(2x+3\right)}
Since \frac{3+3x^{2}}{\left(3x-2\right)\left(2x+3\right)} and \frac{x-5}{\left(3x-2\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{-2+3x^{2}+x}{\left(3x-2\right)\left(2x+3\right)}
Combine like terms in 3+3x^{2}+x-5.
\frac{\left(3x-2\right)\left(x+1\right)}{\left(3x-2\right)\left(2x+3\right)}
Factor the expressions that are not already factored in \frac{-2+3x^{2}+x}{\left(3x-2\right)\left(2x+3\right)}.
\frac{x+1}{2x+3}
Cancel out 3x-2 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}