Question

Simplify the complex fraction .
[(2)/(5t) - (3)/3t)]/[(1)/(2t) + (1)/(2t)]

Answer 1

The simplified form of the given expression
`((2)/(5t)-(3)/(3t) )/((1)/(2t)+(1)/(2t))=-(3)/(5)`

Explanation:

Given expression
`((2)/(5t)-(3)/(3t) )/((1)/(2t)+(1)/(2t)  )`

We have to simplify the given expression
`((2)/(5t)-(3)/(3t) )/((1)/(2t)+(1)/(2t)  )`

Consider the given expression
`((2)/(5t)-(3)/(3t) )/((1)/(2t)+(1)/(2t)  )`

Consider denominator
`(1)/(2t)+(1)/(2t)`

Apply rule,
`(a)/(c)\pm (b)/(c)=(a\pm \:b)/(c)`

`=(1+1)/(2t)=(1)/(t)`

Now, apply fraction rule,
`(a)/((b)/(c))=(a\cdot \:c)/(b)`

We get,

`=(\left((2)/(5t)-(3)/(3t)\right)t)/(1)`

Simplify, we get,

`(t\left((2)/(5t)-(1)/(t)\right))/(1)`

Simplify, we get,

`(t\left((2)/(5t)-(1)/(t)\right))/(1)`

Further simplify by
`(-a)/(b)=-(a)/(b) \ and\  a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

We get,
`=-(3t)/(5t)`

Thus,
`-(3)/(5)`

Answer 2

I hope this helps you