Evaluate
-\frac{1}{5x-3y}
Expand
-\frac{1}{5x-3y}
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\frac{-\left(15x-15y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}+\frac{4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5x-3y\right)\left(5x+3y\right) and -3y-5x is \left(-5x-3y\right)\left(5x-3y\right). Multiply \frac{15x-15y}{\left(5x-3y\right)\left(5x+3y\right)} times \frac{-1}{-1}. Multiply \frac{4}{-3y-5x} times \frac{5x-3y}{5x-3y}.
\frac{-\left(15x-15y\right)+4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
Since \frac{-\left(15x-15y\right)}{\left(-5x-3y\right)\left(5x-3y\right)} and \frac{4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)} have the same denominator, add them by adding their numerators.
\frac{-15x+15y+20x-12y}{\left(-5x-3y\right)\left(5x-3y\right)}
Do the multiplications in -\left(15x-15y\right)+4\left(5x-3y\right).
\frac{5x+3y}{\left(-5x-3y\right)\left(5x-3y\right)}
Combine like terms in -15x+15y+20x-12y.
\frac{-\left(-5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
Extract the negative sign in 5x+3y.
\frac{-1}{5x-3y}
Cancel out -5x-3y in both numerator and denominator.
\frac{-\left(15x-15y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}+\frac{4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5x-3y\right)\left(5x+3y\right) and -3y-5x is \left(-5x-3y\right)\left(5x-3y\right). Multiply \frac{15x-15y}{\left(5x-3y\right)\left(5x+3y\right)} times \frac{-1}{-1}. Multiply \frac{4}{-3y-5x} times \frac{5x-3y}{5x-3y}.
\frac{-\left(15x-15y\right)+4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
Since \frac{-\left(15x-15y\right)}{\left(-5x-3y\right)\left(5x-3y\right)} and \frac{4\left(5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)} have the same denominator, add them by adding their numerators.
\frac{-15x+15y+20x-12y}{\left(-5x-3y\right)\left(5x-3y\right)}
Do the multiplications in -\left(15x-15y\right)+4\left(5x-3y\right).
\frac{5x+3y}{\left(-5x-3y\right)\left(5x-3y\right)}
Combine like terms in -15x+15y+20x-12y.
\frac{-\left(-5x-3y\right)}{\left(-5x-3y\right)\left(5x-3y\right)}
Extract the negative sign in 5x+3y.
\frac{-1}{5x-3y}
Cancel out -5x-3y 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}