Evaluate
\frac{6x+y}{9x-y}
Expand
-\frac{6x+y}{y-9x}
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\frac{-\left(x+y\right)}{-9x+y}-\frac{5x}{-9x+y}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x-y and y-9x is -9x+y. Multiply \frac{x+y}{9x-y} times \frac{-1}{-1}.
\frac{-\left(x+y\right)-5x}{-9x+y}
Since \frac{-\left(x+y\right)}{-9x+y} and \frac{5x}{-9x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{-x-y-5x}{-9x+y}
Do the multiplications in -\left(x+y\right)-5x.
\frac{-6x-y}{-9x+y}
Combine like terms in -x-y-5x.
\frac{-\left(x+y\right)}{-9x+y}-\frac{5x}{-9x+y}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x-y and y-9x is -9x+y. Multiply \frac{x+y}{9x-y} times \frac{-1}{-1}.
\frac{-\left(x+y\right)-5x}{-9x+y}
Since \frac{-\left(x+y\right)}{-9x+y} and \frac{5x}{-9x+y} have the same denominator, subtract them by subtracting their numerators.
\frac{-x-y-5x}{-9x+y}
Do the multiplications in -\left(x+y\right)-5x.
\frac{-6x-y}{-9x+y}
Combine like terms in -x-y-5x.
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}