Answer
no solution
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\dfrac{10}{4x-4}=\dfrac{1}{1-x}
,$ use cross-multiplication. Then use the properties of equality to isolate the variable. Finally, do checking and ensure that any denominator does not become $0.$
$\bf{\text{Solution Details:}}$
Since $\dfrac{a}{b}=\dfrac{c}{d}$ implies $ad=bc$ or sometimes referred to as cross-multiplication, the equation above is equivalent to
\begin{array}{l}\require{cancel}
(10)(1-x)=(4x-4)(1)
\\\\
10-10x=4x-4
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
-10x-4x=-4-10
\\\\
-14x=-14
\\\\
x=\dfrac{-14}{-14}
\\\\
x=1
.\end{array}
If $x=1,$ the part of the given equation, $
\dfrac{1}{1-x}
,$ becomes $
\dfrac{1}{0}
,$ which is undefined. Hence, there is $\text{
no solution
.}$
