Evaluate
\frac{3x+1}{x-5}
Expand
\frac{3x+1}{x-5}
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\frac{2x-1}{x-5}-\frac{-\left(x+2\right)}{x-5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-5 and 5-x is x-5. Multiply \frac{x+2}{5-x} times \frac{-1}{-1}.
\frac{2x-1-\left(-\left(x+2\right)\right)}{x-5}
Since \frac{2x-1}{x-5} and \frac{-\left(x+2\right)}{x-5} have the same denominator, subtract them by subtracting their numerators.
\frac{2x-1+x+2}{x-5}
Do the multiplications in 2x-1-\left(-\left(x+2\right)\right).
\frac{3x+1}{x-5}
Combine like terms in 2x-1+x+2.
\frac{2x-1}{x-5}-\frac{-\left(x+2\right)}{x-5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-5 and 5-x is x-5. Multiply \frac{x+2}{5-x} times \frac{-1}{-1}.
\frac{2x-1-\left(-\left(x+2\right)\right)}{x-5}
Since \frac{2x-1}{x-5} and \frac{-\left(x+2\right)}{x-5} have the same denominator, subtract them by subtracting their numerators.
\frac{2x-1+x+2}{x-5}
Do the multiplications in 2x-1-\left(-\left(x+2\right)\right).
\frac{3x+1}{x-5}
Combine like terms in 2x-1+x+2.
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}