Evaluate
\frac{\left(x+7\right)\left(4x+y\right)}{xy}
Expand
\frac{4x^{2}+xy+28x+7y}{xy}
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\left(x+7\right)\left(\frac{y}{xy}+\frac{4x}{xy}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{4}{y} times \frac{x}{x}.
\left(x+7\right)\times \frac{y+4x}{xy}
Since \frac{y}{xy} and \frac{4x}{xy} have the same denominator, add them by adding their numerators.
\frac{\left(x+7\right)\left(y+4x\right)}{xy}
Express \left(x+7\right)\times \frac{y+4x}{xy} as a single fraction.
\frac{xy+4x^{2}+7y+28x}{xy}
Apply the distributive property by multiplying each term of x+7 by each term of y+4x.
\left(x+7\right)\left(\frac{y}{xy}+\frac{4x}{xy}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{4}{y} times \frac{x}{x}.
\left(x+7\right)\times \frac{y+4x}{xy}
Since \frac{y}{xy} and \frac{4x}{xy} have the same denominator, add them by adding their numerators.
\frac{\left(x+7\right)\left(y+4x\right)}{xy}
Express \left(x+7\right)\times \frac{y+4x}{xy} as a single fraction.
\frac{xy+4x^{2}+7y+28x}{xy}
Apply the distributive property by multiplying each term of x+7 by each term of y+4x.
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}