Evaluate
\frac{17-4x}{2x-1}
Expand
\frac{17-4x}{2x-1}
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\frac{\frac{x+2}{x-3}-\frac{5\left(x-3\right)}{x-3}}{\frac{x+2}{x-3}+1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-3}{x-3}.
\frac{\frac{x+2-5\left(x-3\right)}{x-3}}{\frac{x+2}{x-3}+1}
Since \frac{x+2}{x-3} and \frac{5\left(x-3\right)}{x-3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x+2-5x+15}{x-3}}{\frac{x+2}{x-3}+1}
Do the multiplications in x+2-5\left(x-3\right).
\frac{\frac{-4x+17}{x-3}}{\frac{x+2}{x-3}+1}
Combine like terms in x+2-5x+15.
\frac{\frac{-4x+17}{x-3}}{\frac{x+2}{x-3}+\frac{x-3}{x-3}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-3}{x-3}.
\frac{\frac{-4x+17}{x-3}}{\frac{x+2+x-3}{x-3}}
Since \frac{x+2}{x-3} and \frac{x-3}{x-3} have the same denominator, add them by adding their numerators.
\frac{\frac{-4x+17}{x-3}}{\frac{2x-1}{x-3}}
Combine like terms in x+2+x-3.
\frac{\left(-4x+17\right)\left(x-3\right)}{\left(x-3\right)\left(2x-1\right)}
Divide \frac{-4x+17}{x-3} by \frac{2x-1}{x-3} by multiplying \frac{-4x+17}{x-3} by the reciprocal of \frac{2x-1}{x-3}.
\frac{-4x+17}{2x-1}
Cancel out x-3 in both numerator and denominator.
\frac{\frac{x+2}{x-3}-\frac{5\left(x-3\right)}{x-3}}{\frac{x+2}{x-3}+1}
To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x-3}{x-3}.
\frac{\frac{x+2-5\left(x-3\right)}{x-3}}{\frac{x+2}{x-3}+1}
Since \frac{x+2}{x-3} and \frac{5\left(x-3\right)}{x-3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{x+2-5x+15}{x-3}}{\frac{x+2}{x-3}+1}
Do the multiplications in x+2-5\left(x-3\right).
\frac{\frac{-4x+17}{x-3}}{\frac{x+2}{x-3}+1}
Combine like terms in x+2-5x+15.
\frac{\frac{-4x+17}{x-3}}{\frac{x+2}{x-3}+\frac{x-3}{x-3}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-3}{x-3}.
\frac{\frac{-4x+17}{x-3}}{\frac{x+2+x-3}{x-3}}
Since \frac{x+2}{x-3} and \frac{x-3}{x-3} have the same denominator, add them by adding their numerators.
\frac{\frac{-4x+17}{x-3}}{\frac{2x-1}{x-3}}
Combine like terms in x+2+x-3.
\frac{\left(-4x+17\right)\left(x-3\right)}{\left(x-3\right)\left(2x-1\right)}
Divide \frac{-4x+17}{x-3} by \frac{2x-1}{x-3} by multiplying \frac{-4x+17}{x-3} by the reciprocal of \frac{2x-1}{x-3}.
\frac{-4x+17}{2x-1}
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}