Question

Make q the subject of t =1/p+1/q

Answer 1

The equation with q as the subject is
`q=(p)/(tp-1)`

In mathematics and algebra, "making something the subject of another thing" means rearranging an equation or formula so that a specific variable is isolated on one side of the equation. The goal is to express that variable in terms of the other variables in the equation.

Step 1: Get rid of the fractions by taking the common denominator.

Multiply both sides of the equation by pq to eliminate the denominators.

`t=(1)/(p) +(1)/(q)`

`t * pq= ((1)/(p) +(1)/(q))* pq`

`tpq=q+p`

Step 2: Move the q term to one side of the equation. Subtract q from both sides of the equation.

`tpq-q=p+q-q`

`tpq-q=p`

Step 3: Factor out the q from the left side of the equation.

`q(tp-1)=p`

Finally, solve for q by dividing both sides by
`tp-1`

`q=(p)/(tp-1)`

So, the equation with q as the subject is
`q=(p)/(tp-1)`.