Question

The denominator of a fraction is five more than the numerator. If both the numerator and denominator are decreased by 3, the simplified result is 7/8. Find the original fraction. Do NOT simplify.

Answer 1

We are going to formulate the equation mentioned in the statement

`(x-3)/(x+5-3)=(7)/(8)`

Now let's solve the problem

`\begin{gathered} (x-3)/(x+5-3)=(7)/(8) \\ (x-3)/(x+2)=(7)/(8) \\ 8\left(x-3\right)=7\left(x+2\right) \\ 8x-24=7x+14 \\ 8x-7x=24+14 \\ x=38 \\ \end{gathered}`

Now we calculate the values for the original equation

`\begin{gathered} (38)/(38+5) \\ (38)/(43) \end{gathered}`

The solution would be 38/43