Evaluate
\frac{3k^{3}+6k^{2}+5k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Expand
\frac{3k^{3}+6k^{2}+5k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Quiz
Polynomial
5 problems similar to:
\frac{ 3k }{ 2k+1 } + \frac{ 1 }{ { \left(k+1 \right) }^{ 2 } }
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\frac{3k\left(k+1\right)^{2}}{\left(2k+1\right)\left(k+1\right)^{2}}+\frac{2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2k+1 and \left(k+1\right)^{2} is \left(2k+1\right)\left(k+1\right)^{2}. Multiply \frac{3k}{2k+1} times \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}. Multiply \frac{1}{\left(k+1\right)^{2}} times \frac{2k+1}{2k+1}.
\frac{3k\left(k+1\right)^{2}+2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Since \frac{3k\left(k+1\right)^{2}}{\left(2k+1\right)\left(k+1\right)^{2}} and \frac{2k+1}{\left(2k+1\right)\left(k+1\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{3k^{3}+6k^{2}+3k+2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Do the multiplications in 3k\left(k+1\right)^{2}+2k+1.
\frac{3k^{3}+6k^{2}+5k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Combine like terms in 3k^{3}+6k^{2}+3k+2k+1.
\frac{3k^{3}+6k^{2}+5k+1}{2k^{3}+5k^{2}+4k+1}
Expand \left(2k+1\right)\left(k+1\right)^{2}.
\frac{3k\left(k+1\right)^{2}}{\left(2k+1\right)\left(k+1\right)^{2}}+\frac{2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2k+1 and \left(k+1\right)^{2} is \left(2k+1\right)\left(k+1\right)^{2}. Multiply \frac{3k}{2k+1} times \frac{\left(k+1\right)^{2}}{\left(k+1\right)^{2}}. Multiply \frac{1}{\left(k+1\right)^{2}} times \frac{2k+1}{2k+1}.
\frac{3k\left(k+1\right)^{2}+2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Since \frac{3k\left(k+1\right)^{2}}{\left(2k+1\right)\left(k+1\right)^{2}} and \frac{2k+1}{\left(2k+1\right)\left(k+1\right)^{2}} have the same denominator, add them by adding their numerators.
\frac{3k^{3}+6k^{2}+3k+2k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Do the multiplications in 3k\left(k+1\right)^{2}+2k+1.
\frac{3k^{3}+6k^{2}+5k+1}{\left(2k+1\right)\left(k+1\right)^{2}}
Combine like terms in 3k^{3}+6k^{2}+3k+2k+1.
\frac{3k^{3}+6k^{2}+5k+1}{2k^{3}+5k^{2}+4k+1}
Expand \left(2k+1\right)\left(k+1\right)^{2}.
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}