Evaluate
\frac{3x+4}{x\left(2x+3\right)}
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\frac{3x+4}{x\left(2x+3\right)}
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\frac{4x}{\left(2x-3\right)\left(2x+3\right)}+\frac{1}{x\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Factor 4x^{2}-9. Factor 2x^{2}+3x.
\frac{4xx}{x\left(2x-3\right)\left(2x+3\right)}+\frac{2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2x-3\right)\left(2x+3\right) and x\left(2x+3\right) is x\left(2x-3\right)\left(2x+3\right). Multiply \frac{4x}{\left(2x-3\right)\left(2x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x\left(2x+3\right)} times \frac{2x-3}{2x-3}.
\frac{4xx+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Since \frac{4xx}{x\left(2x-3\right)\left(2x+3\right)} and \frac{2x-3}{x\left(2x-3\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Do the multiplications in 4xx+2x-3.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{x\left(2x-3\right)}
Factor 2x^{2}-3x.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(2x-3\right)\left(2x+3\right) and x\left(2x-3\right) is x\left(2x-3\right)\left(2x+3\right). Multiply \frac{x-3}{x\left(2x-3\right)} times \frac{2x+3}{2x+3}.
\frac{4x^{2}+2x-3+\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)}
Since \frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)} and \frac{\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}+2x-3+2x^{2}+3x-6x-9}{x\left(2x-3\right)\left(2x+3\right)}
Do the multiplications in 4x^{2}+2x-3+\left(x-3\right)\left(2x+3\right).
\frac{6x^{2}-x-12}{x\left(2x-3\right)\left(2x+3\right)}
Combine like terms in 4x^{2}+2x-3+2x^{2}+3x-6x-9.
\frac{\left(2x-3\right)\left(3x+4\right)}{x\left(2x-3\right)\left(2x+3\right)}
Factor the expressions that are not already factored in \frac{6x^{2}-x-12}{x\left(2x-3\right)\left(2x+3\right)}.
\frac{3x+4}{x\left(2x+3\right)}
Cancel out 2x-3 in both numerator and denominator.
\frac{3x+4}{2x^{2}+3x}
Expand x\left(2x+3\right).
\frac{4x}{\left(2x-3\right)\left(2x+3\right)}+\frac{1}{x\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Factor 4x^{2}-9. Factor 2x^{2}+3x.
\frac{4xx}{x\left(2x-3\right)\left(2x+3\right)}+\frac{2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(2x-3\right)\left(2x+3\right) and x\left(2x+3\right) is x\left(2x-3\right)\left(2x+3\right). Multiply \frac{4x}{\left(2x-3\right)\left(2x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x\left(2x+3\right)} times \frac{2x-3}{2x-3}.
\frac{4xx+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Since \frac{4xx}{x\left(2x-3\right)\left(2x+3\right)} and \frac{2x-3}{x\left(2x-3\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{2x^{2}-3x}
Do the multiplications in 4xx+2x-3.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{x-3}{x\left(2x-3\right)}
Factor 2x^{2}-3x.
\frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)}+\frac{\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(2x-3\right)\left(2x+3\right) and x\left(2x-3\right) is x\left(2x-3\right)\left(2x+3\right). Multiply \frac{x-3}{x\left(2x-3\right)} times \frac{2x+3}{2x+3}.
\frac{4x^{2}+2x-3+\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)}
Since \frac{4x^{2}+2x-3}{x\left(2x-3\right)\left(2x+3\right)} and \frac{\left(x-3\right)\left(2x+3\right)}{x\left(2x-3\right)\left(2x+3\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{2}+2x-3+2x^{2}+3x-6x-9}{x\left(2x-3\right)\left(2x+3\right)}
Do the multiplications in 4x^{2}+2x-3+\left(x-3\right)\left(2x+3\right).
\frac{6x^{2}-x-12}{x\left(2x-3\right)\left(2x+3\right)}
Combine like terms in 4x^{2}+2x-3+2x^{2}+3x-6x-9.
\frac{\left(2x-3\right)\left(3x+4\right)}{x\left(2x-3\right)\left(2x+3\right)}
Factor the expressions that are not already factored in \frac{6x^{2}-x-12}{x\left(2x-3\right)\left(2x+3\right)}.
\frac{3x+4}{x\left(2x+3\right)}
Cancel out 2x-3 in both numerator and denominator.
\frac{3x+4}{2x^{2}+3x}
Expand x\left(2x+3\right).
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}