Question

Solve for y. y/m + y/n = p

y= (n+m)/mnp
y= mnp/(m+n)
y = mn/p

isnt it p/mn? but thats not an answer.

Answer 1

Given :

$\boxed{ \rm \frac{y}{m} + \frac{y}{n} = p}$

To find:

• Value of y

Step by step expansion:

$\dashrightarrow \sf\dfrac{y}{m} + \dfrac{y}{n} = p$

write the equation

$\dashrightarrow \sf \dfrac{\frac{y \times mn}{m} + \frac{y \times mn}{n}}{mn} = p$

Add y/n with y/n and we will get Lcm as mn

$\dashrightarrow \sf \dfrac{\frac{y \times \cancel mn}{\cancel m} + \frac{y \times m\cancel n}{\cancel n}}{mn} = p$

Cancel the similar terms

$\dashrightarrow \sf \dfrac{\frac{y \times n}{1} + \frac{y \times m}{1}}{mn} = p$

$\dashrightarrow \sf \dfrac{yn + ym}{mn} = p$

remove 1 as denominator

$\dashrightarrow \sf \dfrac{y(n + m)}{mn} = p$

take y as common

$\dashrightarrow \sf \dfrac{(n + m)}{mn} = \dfrac{p}{y}$

transfer y to other side as denominator of p

$\dashrightarrow \sf \dfrac{mn}{(n + m)} = \dfrac{y}{p}$

reciprocal the whole equation

$\dashrightarrow \sf \dfrac{mnp}{(n + m)} = \dfrac{y}{1}$

transfer p other side as numerator

$\dashrightarrow \boxed{ \bf y = \dfrac{mnp}{(n + m)} }$

$\therefore \red {\underline {\textbf{\textsf{Option 2 i.e \{y= mnp/(m+n) \} is correct }}}}$

Answer 2

The value of y from the given expression is y  = mnp/n+m

Subject of formula

Given the following expression

y/m + y/n = p

We are to make y the subject of the formula

yn+ym/mn = p

yn + ym = mnp
y(n+m) = mnp

Divide both sides by n+m

y(n+m)/nmp = mnp/n+m
y  = mnp/n+m

Hence the value of y from the given expression is y  = mnp/n+m

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