Question

P=1/2

q=-1/3

r=1/5


30pqr(p+q+r)/(p+q)(p+r)


Answer -22/7

Answer 1

Given:

• 
  `p=\frac12`
• 
  `q=-\frac13`
• 
  `r=\frac15`

Given expression:

`(30pqr(p+q+r))/((p+q)(p+r))`

Substitute given values into given expression:

`\implies (30\cdot\frac12\cdot-\frac13\cdot\frac15\left(\frac12-\frac13+\frac15\right))/(\left(\frac12-\frac13\right)\left(\frac12+\frac15\right))`

`\implies (-(30)/(30)\left((15)/(30)-(10)/(30)+(6)/(30)\right))/(\left(\frac36-\frac26\right)\left((5)/(10)+(2)/(10)\right))`

`\implies (-1\left((11)/(30)\right))/(\left(\frac16\right)\left((7)/(10)\right))`

`\implies (-(11)/(30))/((7)/(60))`

`\implies -(11)/(30)* (60)/(7)`

`\implies -(660)/(210)`

`\implies -(22)/(7)`