Evaluate
\frac{3x^{2}-4x+3}{3\left(x-1\right)}
Expand
\frac{3x^{2}-4x+3}{3\left(x-1\right)}
Graph
Share
Copied to clipboard
\frac{\frac{2}{x-1}-\frac{x-1}{x-1}}{3}+x
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-1}{x-1}.
\frac{\frac{2-\left(x-1\right)}{x-1}}{3}+x
Since \frac{2}{x-1} and \frac{x-1}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2-x+1}{x-1}}{3}+x
Do the multiplications in 2-\left(x-1\right).
\frac{\frac{3-x}{x-1}}{3}+x
Combine like terms in 2-x+1.
\frac{3-x}{\left(x-1\right)\times 3}+x
Express \frac{\frac{3-x}{x-1}}{3} as a single fraction.
\frac{3-x}{\left(x-1\right)\times 3}+\frac{x\left(x-1\right)\times 3}{\left(x-1\right)\times 3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)\times 3}{\left(x-1\right)\times 3}.
\frac{3-x+x\left(x-1\right)\times 3}{\left(x-1\right)\times 3}
Since \frac{3-x}{\left(x-1\right)\times 3} and \frac{x\left(x-1\right)\times 3}{\left(x-1\right)\times 3} have the same denominator, add them by adding their numerators.
\frac{3-x+3x^{2}-3x}{\left(x-1\right)\times 3}
Do the multiplications in 3-x+x\left(x-1\right)\times 3.
\frac{3-4x+3x^{2}}{\left(x-1\right)\times 3}
Combine like terms in 3-x+3x^{2}-3x.
\frac{3-4x+3x^{2}}{3x-3}
Expand \left(x-1\right)\times 3.
\frac{\frac{2}{x-1}-\frac{x-1}{x-1}}{3}+x
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-1}{x-1}.
\frac{\frac{2-\left(x-1\right)}{x-1}}{3}+x
Since \frac{2}{x-1} and \frac{x-1}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2-x+1}{x-1}}{3}+x
Do the multiplications in 2-\left(x-1\right).
\frac{\frac{3-x}{x-1}}{3}+x
Combine like terms in 2-x+1.
\frac{3-x}{\left(x-1\right)\times 3}+x
Express \frac{\frac{3-x}{x-1}}{3} as a single fraction.
\frac{3-x}{\left(x-1\right)\times 3}+\frac{x\left(x-1\right)\times 3}{\left(x-1\right)\times 3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)\times 3}{\left(x-1\right)\times 3}.
\frac{3-x+x\left(x-1\right)\times 3}{\left(x-1\right)\times 3}
Since \frac{3-x}{\left(x-1\right)\times 3} and \frac{x\left(x-1\right)\times 3}{\left(x-1\right)\times 3} have the same denominator, add them by adding their numerators.
\frac{3-x+3x^{2}-3x}{\left(x-1\right)\times 3}
Do the multiplications in 3-x+x\left(x-1\right)\times 3.
\frac{3-4x+3x^{2}}{\left(x-1\right)\times 3}
Combine like terms in 3-x+3x^{2}-3x.
\frac{3-4x+3x^{2}}{3x-3}
Expand \left(x-1\right)\times 3.
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}