Evaluate
\frac{3\left(4x+5\right)}{\left(x+2\right)\left(4x+9\right)}
Expand
\frac{3\left(4x+5\right)}{\left(x+2\right)\left(4x+9\right)}
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\frac{3\left(4x+5\right)}{\left(x+2\right)\left(4x+9\right)}
Multiply \frac{3}{x+2} times \frac{4x+5}{4x+9} by multiplying numerator times numerator and denominator times denominator.
\frac{12x+15}{\left(x+2\right)\left(4x+9\right)}
Use the distributive property to multiply 3 by 4x+5.
\frac{12x+15}{4x^{2}+9x+8x+18}
Apply the distributive property by multiplying each term of x+2 by each term of 4x+9.
\frac{12x+15}{4x^{2}+17x+18}
Combine 9x and 8x to get 17x.
\frac{3\left(4x+5\right)}{\left(x+2\right)\left(4x+9\right)}
Multiply \frac{3}{x+2} times \frac{4x+5}{4x+9} by multiplying numerator times numerator and denominator times denominator.
\frac{12x+15}{\left(x+2\right)\left(4x+9\right)}
Use the distributive property to multiply 3 by 4x+5.
\frac{12x+15}{4x^{2}+9x+8x+18}
Apply the distributive property by multiplying each term of x+2 by each term of 4x+9.
\frac{12x+15}{4x^{2}+17x+18}
Combine 9x and 8x to get 17x.
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}