Question

Question #b55d3

Answer 1

`2p/q=-3p/q^2+5/q-1`

Explanation:

Write as:`" "2p=-3q/p-q+5`

To 'force' the left hand side into the target format divide both sides by q.

`2p/q=-3p/q^2-1+5/q`

Write as:

`2p/q=-3p/q^2+5/q-1`

Answer 2

Assuming `p,q!=0`, I got `color(red)(2p/q=(4p^2/q+2p+6)/5)`

Explanation:

Given
`color(white)("XXX")2p+3q/p+q=5`

Multiplying both sides by `color(blue)(p/q)`
`color(white)("XXX")2p * color(blue)(p/q) +3q/p * color(blue)(p/q) + q * color(blue)(p/q) = 5 * color(blue)(p/q)`

`color(white)("XXX")2p^2/q+3+p=5p/q`

Multiplying both sides by `color(green)(2/5)`
`color(white)("XXX")2p^2/q * color(green)(2/5)+3 * color(green)(2/5) +p * color(green)(2/5) = 5p/q * color(green)(2/5)`

`color(white)("XXX")(4p^2/q+6+2p)/5=2p/q`

`color(white)("XXX")2p/q=(4p^2/q+2p+6)/5`