Evaluate
\frac{6x^{2}+11x-15}{4x^{2}-25}
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\frac{6x^{2}+11x-15}{4x^{2}-25}
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\frac{3x}{2x-5}-\frac{4x+15}{4x^{2}-25}
Express 3\times \frac{x}{2x-5} as a single fraction.
\frac{3x}{2x-5}-\frac{4x+15}{\left(2x-5\right)\left(2x+5\right)}
Factor 4x^{2}-25.
\frac{3x\left(2x+5\right)}{\left(2x-5\right)\left(2x+5\right)}-\frac{4x+15}{\left(2x-5\right)\left(2x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-5 and \left(2x-5\right)\left(2x+5\right) is \left(2x-5\right)\left(2x+5\right). Multiply \frac{3x}{2x-5} times \frac{2x+5}{2x+5}.
\frac{3x\left(2x+5\right)-\left(4x+15\right)}{\left(2x-5\right)\left(2x+5\right)}
Since \frac{3x\left(2x+5\right)}{\left(2x-5\right)\left(2x+5\right)} and \frac{4x+15}{\left(2x-5\right)\left(2x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x^{2}+15x-4x-15}{\left(2x-5\right)\left(2x+5\right)}
Do the multiplications in 3x\left(2x+5\right)-\left(4x+15\right).
\frac{6x^{2}+11x-15}{\left(2x-5\right)\left(2x+5\right)}
Combine like terms in 6x^{2}+15x-4x-15.
\frac{6x^{2}+11x-15}{4x^{2}-25}
Expand \left(2x-5\right)\left(2x+5\right).
\frac{3x}{2x-5}-\frac{4x+15}{4x^{2}-25}
Express 3\times \frac{x}{2x-5} as a single fraction.
\frac{3x}{2x-5}-\frac{4x+15}{\left(2x-5\right)\left(2x+5\right)}
Factor 4x^{2}-25.
\frac{3x\left(2x+5\right)}{\left(2x-5\right)\left(2x+5\right)}-\frac{4x+15}{\left(2x-5\right)\left(2x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-5 and \left(2x-5\right)\left(2x+5\right) is \left(2x-5\right)\left(2x+5\right). Multiply \frac{3x}{2x-5} times \frac{2x+5}{2x+5}.
\frac{3x\left(2x+5\right)-\left(4x+15\right)}{\left(2x-5\right)\left(2x+5\right)}
Since \frac{3x\left(2x+5\right)}{\left(2x-5\right)\left(2x+5\right)} and \frac{4x+15}{\left(2x-5\right)\left(2x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{6x^{2}+15x-4x-15}{\left(2x-5\right)\left(2x+5\right)}
Do the multiplications in 3x\left(2x+5\right)-\left(4x+15\right).
\frac{6x^{2}+11x-15}{\left(2x-5\right)\left(2x+5\right)}
Combine like terms in 6x^{2}+15x-4x-15.
\frac{6x^{2}+11x-15}{4x^{2}-25}
Expand \left(2x-5\right)\left(2x+5\right).
Examples
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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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