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Simplify the expression $\frac{\frac{x-1}{2x-1}\left(2\left(x-1\right)-\left(2x-1\right)\right)}{\left(x-1\right)^2}$

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Solution

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Final Answer

$\frac{-1}{\left(2x-1\right)\left(x-1\right)}$
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Step-by-step Solution

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Multiplying the fraction by $2\left(x-1\right)-\left(2x-1\right)$

$\frac{\frac{\left(x-1\right)\left(2\left(x-1\right)-\left(2x-1\right)\right)}{2x-1}}{\left(x-1\right)^2}$

Learn how to solve simplification of algebraic fractions problems step by step online.

$\frac{\frac{\left(x-1\right)\left(2\left(x-1\right)-\left(2x-1\right)\right)}{2x-1}}{\left(x-1\right)^2}$

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Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression ((x-1)/(2x-1)(2(x-1)-(2x-1)))/((x-1)^2). Multiplying the fraction by 2\left(x-1\right)-\left(2x-1\right). Divide fractions \frac{\frac{\left(x-1\right)\left(2\left(x-1\right)-\left(2x-1\right)\right)}{2x-1}}{\left(x-1\right)^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Simplify the fraction by x-1. Simplify the product -(2x-1).

Final Answer

$\frac{-1}{\left(2x-1\right)\left(x-1\right)}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x-1)/(2x-1)(2(x-1)+-1(2x-1))/((x-1)^2) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $\frac{-1}{\left(2x-1\right)\left(x-1\right)}$

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x
y
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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