Evaluate
\frac{3x+10y}{4\left(5x+6y\right)}
Expand
\frac{3x+10y}{4\left(5x+6y\right)}
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\frac{3}{4}-\frac{3x+2y}{5x+6y}
Cancel out x in both numerator and denominator.
\frac{3\left(5x+6y\right)}{4\left(5x+6y\right)}-\frac{4\left(3x+2y\right)}{4\left(5x+6y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 5x+6y is 4\left(5x+6y\right). Multiply \frac{3}{4} times \frac{5x+6y}{5x+6y}. Multiply \frac{3x+2y}{5x+6y} times \frac{4}{4}.
\frac{3\left(5x+6y\right)-4\left(3x+2y\right)}{4\left(5x+6y\right)}
Since \frac{3\left(5x+6y\right)}{4\left(5x+6y\right)} and \frac{4\left(3x+2y\right)}{4\left(5x+6y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{15x+18y-12x-8y}{4\left(5x+6y\right)}
Do the multiplications in 3\left(5x+6y\right)-4\left(3x+2y\right).
\frac{3x+10y}{4\left(5x+6y\right)}
Combine like terms in 15x+18y-12x-8y.
\frac{3x+10y}{20x+24y}
Expand 4\left(5x+6y\right).
\frac{3}{4}-\frac{3x+2y}{5x+6y}
Cancel out x in both numerator and denominator.
\frac{3\left(5x+6y\right)}{4\left(5x+6y\right)}-\frac{4\left(3x+2y\right)}{4\left(5x+6y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 5x+6y is 4\left(5x+6y\right). Multiply \frac{3}{4} times \frac{5x+6y}{5x+6y}. Multiply \frac{3x+2y}{5x+6y} times \frac{4}{4}.
\frac{3\left(5x+6y\right)-4\left(3x+2y\right)}{4\left(5x+6y\right)}
Since \frac{3\left(5x+6y\right)}{4\left(5x+6y\right)} and \frac{4\left(3x+2y\right)}{4\left(5x+6y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{15x+18y-12x-8y}{4\left(5x+6y\right)}
Do the multiplications in 3\left(5x+6y\right)-4\left(3x+2y\right).
\frac{3x+10y}{4\left(5x+6y\right)}
Combine like terms in 15x+18y-12x-8y.
\frac{3x+10y}{20x+24y}
Expand 4\left(5x+6y\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}