Evaluate
\frac{3y\left(y-3\right)}{\left(y-36\right)\left(y-4\right)}
Expand
\frac{3\left(y^{2}-3y\right)}{\left(y-36\right)\left(y-4\right)}
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\frac{\frac{y+8}{\left(y-4\right)\left(y+8\right)}+\frac{2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-4 and y+8 is \left(y-4\right)\left(y+8\right). Multiply \frac{1}{y-4} times \frac{y+8}{y+8}. Multiply \frac{2}{y+8} times \frac{y-4}{y-4}.
\frac{\frac{y+8+2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Since \frac{y+8}{\left(y-4\right)\left(y+8\right)} and \frac{2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{y+8+2y-8}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Do the multiplications in y+8+2\left(y-4\right).
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Combine like terms in y+8+2y-8.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4\left(y-3\right)}{\left(y-3\right)\left(y+8\right)}-\frac{3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+8 and y-3 is \left(y-3\right)\left(y+8\right). Multiply \frac{4}{y+8} times \frac{y-3}{y-3}. Multiply \frac{3}{y-3} times \frac{y+8}{y+8}.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4\left(y-3\right)-3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)}}
Since \frac{4\left(y-3\right)}{\left(y-3\right)\left(y+8\right)} and \frac{3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4y-12-3y-24}{\left(y-3\right)\left(y+8\right)}}
Do the multiplications in 4\left(y-3\right)-3\left(y+8\right).
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{y-36}{\left(y-3\right)\left(y+8\right)}}
Combine like terms in 4y-12-3y-24.
\frac{3y\left(y-3\right)\left(y+8\right)}{\left(y-4\right)\left(y+8\right)\left(y-36\right)}
Divide \frac{3y}{\left(y-4\right)\left(y+8\right)} by \frac{y-36}{\left(y-3\right)\left(y+8\right)} by multiplying \frac{3y}{\left(y-4\right)\left(y+8\right)} by the reciprocal of \frac{y-36}{\left(y-3\right)\left(y+8\right)}.
\frac{3y\left(y-3\right)}{\left(y-36\right)\left(y-4\right)}
Cancel out y+8 in both numerator and denominator.
\frac{3y^{2}-9y}{\left(y-36\right)\left(y-4\right)}
Use the distributive property to multiply 3y by y-3.
\frac{3y^{2}-9y}{y^{2}-4y-36y+144}
Apply the distributive property by multiplying each term of y-36 by each term of y-4.
\frac{3y^{2}-9y}{y^{2}-40y+144}
Combine -4y and -36y to get -40y.
\frac{\frac{y+8}{\left(y-4\right)\left(y+8\right)}+\frac{2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y-4 and y+8 is \left(y-4\right)\left(y+8\right). Multiply \frac{1}{y-4} times \frac{y+8}{y+8}. Multiply \frac{2}{y+8} times \frac{y-4}{y-4}.
\frac{\frac{y+8+2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Since \frac{y+8}{\left(y-4\right)\left(y+8\right)} and \frac{2\left(y-4\right)}{\left(y-4\right)\left(y+8\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{y+8+2y-8}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Do the multiplications in y+8+2\left(y-4\right).
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4}{y+8}-\frac{3}{y-3}}
Combine like terms in y+8+2y-8.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4\left(y-3\right)}{\left(y-3\right)\left(y+8\right)}-\frac{3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+8 and y-3 is \left(y-3\right)\left(y+8\right). Multiply \frac{4}{y+8} times \frac{y-3}{y-3}. Multiply \frac{3}{y-3} times \frac{y+8}{y+8}.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4\left(y-3\right)-3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)}}
Since \frac{4\left(y-3\right)}{\left(y-3\right)\left(y+8\right)} and \frac{3\left(y+8\right)}{\left(y-3\right)\left(y+8\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{4y-12-3y-24}{\left(y-3\right)\left(y+8\right)}}
Do the multiplications in 4\left(y-3\right)-3\left(y+8\right).
\frac{\frac{3y}{\left(y-4\right)\left(y+8\right)}}{\frac{y-36}{\left(y-3\right)\left(y+8\right)}}
Combine like terms in 4y-12-3y-24.
\frac{3y\left(y-3\right)\left(y+8\right)}{\left(y-4\right)\left(y+8\right)\left(y-36\right)}
Divide \frac{3y}{\left(y-4\right)\left(y+8\right)} by \frac{y-36}{\left(y-3\right)\left(y+8\right)} by multiplying \frac{3y}{\left(y-4\right)\left(y+8\right)} by the reciprocal of \frac{y-36}{\left(y-3\right)\left(y+8\right)}.
\frac{3y\left(y-3\right)}{\left(y-36\right)\left(y-4\right)}
Cancel out y+8 in both numerator and denominator.
\frac{3y^{2}-9y}{\left(y-36\right)\left(y-4\right)}
Use the distributive property to multiply 3y by y-3.
\frac{3y^{2}-9y}{y^{2}-4y-36y+144}
Apply the distributive property by multiplying each term of y-36 by each term of y-4.
\frac{3y^{2}-9y}{y^{2}-40y+144}
Combine -4y and -36y to get -40y.
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}