Answer
$\dfrac{7}{8}$
Work Step by Step
Let $x$ be the numerator. Then the denominator is $x+1.$
The conditions of the problem translate to
\begin{array}{l}\require{cancel}
\dfrac{x-3}{x+1-3}=\dfrac{4}{5}
\\\\
\dfrac{x-3}{x-2}=\dfrac{4}{5}
.\end{array}
By cross-multiplication and by using the properties of equality, then
\begin{array}{l}\require{cancel}
5(x-3)=4(x-2)
\\\\
5x-15=4x-8
\\\\
5x-4x=-8+15
\\\\
x=7
.\end{array}
Hence, the numerator, $x,$ is $7$ and the denominator, $x+1,$ is $8.$ Hence, the fraction is $
\dfrac{7}{8}
.$
