Evaluate
-\frac{3a-7}{2-5a}
Expand
-\frac{3a-7}{2-5a}
Quiz
Polynomial
5 problems similar to:
\frac { 3 - \frac { 4 } { a - 1 } } { 5 - \frac { 3 } { 1 - a } }
Share
Copied to clipboard
\frac{\frac{3\left(a-1\right)}{a-1}-\frac{4}{a-1}}{5-\frac{3}{1-a}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a-1}{a-1}.
\frac{\frac{3\left(a-1\right)-4}{a-1}}{5-\frac{3}{1-a}}
Since \frac{3\left(a-1\right)}{a-1} and \frac{4}{a-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3a-3-4}{a-1}}{5-\frac{3}{1-a}}
Do the multiplications in 3\left(a-1\right)-4.
\frac{\frac{3a-7}{a-1}}{5-\frac{3}{1-a}}
Combine like terms in 3a-3-4.
\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)}{1-a}-\frac{3}{1-a}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1-a}{1-a}.
\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)-3}{1-a}}
Since \frac{5\left(1-a\right)}{1-a} and \frac{3}{1-a} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3a-7}{a-1}}{\frac{5-5a-3}{1-a}}
Do the multiplications in 5\left(1-a\right)-3.
\frac{\frac{3a-7}{a-1}}{\frac{2-5a}{1-a}}
Combine like terms in 5-5a-3.
\frac{\left(3a-7\right)\left(1-a\right)}{\left(a-1\right)\left(2-5a\right)}
Divide \frac{3a-7}{a-1} by \frac{2-5a}{1-a} by multiplying \frac{3a-7}{a-1} by the reciprocal of \frac{2-5a}{1-a}.
\frac{-\left(a-1\right)\left(3a-7\right)}{\left(a-1\right)\left(-5a+2\right)}
Extract the negative sign in 1-a.
\frac{-\left(3a-7\right)}{-5a+2}
Cancel out a-1 in both numerator and denominator.
\frac{-3a-\left(-7\right)}{-5a+2}
To find the opposite of 3a-7, find the opposite of each term.
\frac{-3a+7}{-5a+2}
The opposite of -7 is 7.
\frac{\frac{3\left(a-1\right)}{a-1}-\frac{4}{a-1}}{5-\frac{3}{1-a}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{a-1}{a-1}.
\frac{\frac{3\left(a-1\right)-4}{a-1}}{5-\frac{3}{1-a}}
Since \frac{3\left(a-1\right)}{a-1} and \frac{4}{a-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3a-3-4}{a-1}}{5-\frac{3}{1-a}}
Do the multiplications in 3\left(a-1\right)-4.
\frac{\frac{3a-7}{a-1}}{5-\frac{3}{1-a}}
Combine like terms in 3a-3-4.
\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)}{1-a}-\frac{3}{1-a}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{1-a}{1-a}.
\frac{\frac{3a-7}{a-1}}{\frac{5\left(1-a\right)-3}{1-a}}
Since \frac{5\left(1-a\right)}{1-a} and \frac{3}{1-a} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3a-7}{a-1}}{\frac{5-5a-3}{1-a}}
Do the multiplications in 5\left(1-a\right)-3.
\frac{\frac{3a-7}{a-1}}{\frac{2-5a}{1-a}}
Combine like terms in 5-5a-3.
\frac{\left(3a-7\right)\left(1-a\right)}{\left(a-1\right)\left(2-5a\right)}
Divide \frac{3a-7}{a-1} by \frac{2-5a}{1-a} by multiplying \frac{3a-7}{a-1} by the reciprocal of \frac{2-5a}{1-a}.
\frac{-\left(a-1\right)\left(3a-7\right)}{\left(a-1\right)\left(-5a+2\right)}
Extract the negative sign in 1-a.
\frac{-\left(3a-7\right)}{-5a+2}
Cancel out a-1 in both numerator and denominator.
\frac{-3a-\left(-7\right)}{-5a+2}
To find the opposite of 3a-7, find the opposite of each term.
\frac{-3a+7}{-5a+2}
The opposite of -7 is 7.
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}