Question

Make y the subject of the following :

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Answer 1

y =
`(-mn)/(m-p^2)`

Explanation:

Given

`\sqrt{(m(y+n))/(y) }` = p ( square both sides )

`(m(y+n))/(y)` = p² ( multiply both sides by y )

m(y + n) = p²y ← distribute parenthesis on left side

my + mn = p²y ( subtract p²y from both sides )

my - p²y + mn = 0 ( subtract mn from both sides )

my - p²y = - mn ← factor out y from each term on the left side

y(m - p²) = - mn ← divide both sides by (m - p²)

y =
`(-mn)/(m-p^2)`

Answer 2

Explanation:

we first square both sides to eliminate the square root brackets..

(√(m(y+n)/y)²= p²

m(y+n)/y = p²

(my +mn)/y =p²

so we multiply both sides by y to eliminate the denominator,

(my+mn)/y*y =p²*y

my+mn = p²y

collecting like terms,we have:

mn= p²y-my

so we seperate the y on the right hand side from the rest to have

mn = y(p²-m)

so divided both sides by the value in the bracket on the right hand side we have..

mn/(p²-m)=y(p²-m)/(p²-m)

so we have,

y= mn/(p²-m)