Question

How do you solve `5/(b-5)=3/b`?

Answer 1

`b=-15/2`

Explanation:

First we cross multiply and get:
`3(b-5)=5b`

Then we distribute the 3 on the left side
`3b-15=5b`

Now we collect terms by subtracting `3b` from both sides.
`-15=2b`

Divide both sides by 2.
`-15/2=b` which is our answer.

Answer 2

`b=-15/2.`

Explanation:

`5/(b-5)=3/b.`
Multiplying by `b(b-5)` on both sides, we get,
`b(b-5)*5/(b-5)=b(b-5)*3/b`
`:. (5b(b-5))/(b-5)=(3b(b-5))/b`
`:. 5bcancel(b-5)/cancel(b-5)=3cancelb(b-5)/cancel(b)`
`:. 5b=3(b-5)`
`:. 5b=3b-15`
Adding, (-3b) on both sides, `5b-3b=3b-15-3b`
`:. 2b=cancel3b-15-cancel3b`
`:. 2b=-15`
Multiplying by `1/2`,
`1/2(2b)=1/2(-15)`
`1/cancel2cancel2b=-15/2`
`:. b=-15/2.`
This is the reqd. soln. Enjoy, Maths.!