Evaluate
\frac{g^{2}+9g-1}{\left(g-1\right)\left(2g+1\right)}
Expand
\frac{g^{2}+9g-1}{\left(g-1\right)\left(2g+1\right)}
Share
Copied to clipboard
\frac{\left(g+2\right)\left(2g+1\right)}{\left(g-1\right)\left(2g+1\right)}-\frac{\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of g-1 and 2g+1 is \left(g-1\right)\left(2g+1\right). Multiply \frac{g+2}{g-1} times \frac{2g+1}{2g+1}. Multiply \frac{g-3}{2g+1} times \frac{g-1}{g-1}.
\frac{\left(g+2\right)\left(2g+1\right)-\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)}
Since \frac{\left(g+2\right)\left(2g+1\right)}{\left(g-1\right)\left(2g+1\right)} and \frac{\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2g^{2}+g+4g+2-g^{2}+g+3g-3}{\left(g-1\right)\left(2g+1\right)}
Do the multiplications in \left(g+2\right)\left(2g+1\right)-\left(g-3\right)\left(g-1\right).
\frac{g^{2}+9g-1}{\left(g-1\right)\left(2g+1\right)}
Combine like terms in 2g^{2}+g+4g+2-g^{2}+g+3g-3.
\frac{g^{2}+9g-1}{2g^{2}-g-1}
Expand \left(g-1\right)\left(2g+1\right).
\frac{\left(g+2\right)\left(2g+1\right)}{\left(g-1\right)\left(2g+1\right)}-\frac{\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of g-1 and 2g+1 is \left(g-1\right)\left(2g+1\right). Multiply \frac{g+2}{g-1} times \frac{2g+1}{2g+1}. Multiply \frac{g-3}{2g+1} times \frac{g-1}{g-1}.
\frac{\left(g+2\right)\left(2g+1\right)-\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)}
Since \frac{\left(g+2\right)\left(2g+1\right)}{\left(g-1\right)\left(2g+1\right)} and \frac{\left(g-3\right)\left(g-1\right)}{\left(g-1\right)\left(2g+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{2g^{2}+g+4g+2-g^{2}+g+3g-3}{\left(g-1\right)\left(2g+1\right)}
Do the multiplications in \left(g+2\right)\left(2g+1\right)-\left(g-3\right)\left(g-1\right).
\frac{g^{2}+9g-1}{\left(g-1\right)\left(2g+1\right)}
Combine like terms in 2g^{2}+g+4g+2-g^{2}+g+3g-3.
\frac{g^{2}+9g-1}{2g^{2}-g-1}
Expand \left(g-1\right)\left(2g+1\right).
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}