Answer:
The simplified form of the given expression \(\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t}}=-\frac{3}{5}\)
Step-by-step explanation:
Given expression \(\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }\)
We have to simplify the given expression \(\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }\)
Consider the given expression \(\dfrac{\frac{2}{5t}-\frac{3}{3t} }{\frac{1}{2t}+\frac{1}{2t} }\)
Consider denominator \(\frac{1}{2t}+\frac{1}{2t}\)
Apply rule, \(\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\)
\(=\frac{1+1}{2t}=\frac{1}{t}\)
Now, apply fraction rule, \(\frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}\)
We get,
\(=\frac{\left(\frac{2}{5t}-\frac{3}{3t}\right)t}{1}\)
Simplify, we get,
\(\frac{t\left(\frac{2}{5t}-\frac{1}{t}\right)}{1}\)
Simplify, we get,
\(\frac{t\left(\frac{2}{5t}-\frac{1}{t}\right)}{1}\)
Further simplify by \(\frac{-a}{b}=-\frac{a}{b} \ and\ a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\)
We get, \(=-\frac{3t}{5t}\)
Thus, \(-\frac{3}{5}\)
