## College Algebra (11th Edition)

$\bf{\text{Solution Outline:}}$ 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 $\text{ no solution .}$