Literal Equations and Formulas

Question

x/p+x/q=s

 

Answer 1

Hi Alissa,

 

Any time you have an equation with fractions, the easiest way to deal with it is to simply multiply both sides by the denominators.  So, the first thing you want to do is multiply both sides by one of the denominators (let's start with q):

 

x/p + x/q = s,

 

q*(x/p + x/q) = q*s.

 

Distributing q on the left gives you

 

xq/p + xq/q = qs.

 

The second fraction can be reduced to just x:

 

xq/p + x = qs.

 

Then, we want to get rid of the p that's in the first denominator, so we multiply both sides of the equation by p:

 

p*(xq/p + x) = p*qs.

 

Distributing again, we get

 

xqp/p + xp = pqs.

 

The first fraction can be reduced this time, since both the numerator and denominator have a factor of p, so the entire equation simplifies to

 

xq + xp = pqs.

 

Finally, we want to isolate x, and the easiest way to do that in this problem is just to factor it out (it's the greatest common factor on the left hand side):

 

x(q + p) = pqs.

 

And the last step in isolating x is just to divide both sides by the factor (q + p):

 

x(q + p)/(q + p) = pqs/(q + p),

 

which simplifies to

 

x = pqs/(q + p).

 

Hope this helps!

Answer 2

Multiply to get common factors:

 

(x/p) times q

(x/q) times p

s times qp

 

xq/pq + xp/pq = sqp

x(p+q) = s(p^2)(q^2)

x = (s(p^2)(q^2))/(p+q)