Evaluate
\frac{2\left(x^{2}+5x+3\right)}{\left(x+1\right)\left(x+2\right)}
Expand
\frac{2\left(x^{2}+5x+3\right)}{\left(x+1\right)\left(x+2\right)}
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2\left(\frac{x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x+2 is \left(x+1\right)\left(x+2\right). Multiply \frac{x}{x+1} times \frac{x+2}{x+2}. Multiply \frac{3}{x+2} times \frac{x+1}{x+1}.
2\times \frac{x\left(x+2\right)+3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
Since \frac{x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
2\times \frac{x^{2}+2x+3x+3}{\left(x+1\right)\left(x+2\right)}
Do the multiplications in x\left(x+2\right)+3\left(x+1\right).
2\times \frac{x^{2}+5x+3}{\left(x+1\right)\left(x+2\right)}
Combine like terms in x^{2}+2x+3x+3.
\frac{2\left(x^{2}+5x+3\right)}{\left(x+1\right)\left(x+2\right)}
Express 2\times \frac{x^{2}+5x+3}{\left(x+1\right)\left(x+2\right)} as a single fraction.
\frac{2x^{2}+10x+6}{\left(x+1\right)\left(x+2\right)}
Use the distributive property to multiply 2 by x^{2}+5x+3.
\frac{2x^{2}+10x+6}{x^{2}+2x+x+2}
Apply the distributive property by multiplying each term of x+1 by each term of x+2.
\frac{2x^{2}+10x+6}{x^{2}+3x+2}
Combine 2x and x to get 3x.
2\left(\frac{x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x+2 is \left(x+1\right)\left(x+2\right). Multiply \frac{x}{x+1} times \frac{x+2}{x+2}. Multiply \frac{3}{x+2} times \frac{x+1}{x+1}.
2\times \frac{x\left(x+2\right)+3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}
Since \frac{x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)} and \frac{3\left(x+1\right)}{\left(x+1\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
2\times \frac{x^{2}+2x+3x+3}{\left(x+1\right)\left(x+2\right)}
Do the multiplications in x\left(x+2\right)+3\left(x+1\right).
2\times \frac{x^{2}+5x+3}{\left(x+1\right)\left(x+2\right)}
Combine like terms in x^{2}+2x+3x+3.
\frac{2\left(x^{2}+5x+3\right)}{\left(x+1\right)\left(x+2\right)}
Express 2\times \frac{x^{2}+5x+3}{\left(x+1\right)\left(x+2\right)} as a single fraction.
\frac{2x^{2}+10x+6}{\left(x+1\right)\left(x+2\right)}
Use the distributive property to multiply 2 by x^{2}+5x+3.
\frac{2x^{2}+10x+6}{x^{2}+2x+x+2}
Apply the distributive property by multiplying each term of x+1 by each term of x+2.
\frac{2x^{2}+10x+6}{x^{2}+3x+2}
Combine 2x and x to get 3x.
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}