Question

1/y+z+1/z+x+1/x+y=1 andx+y+z=4 Prove that x/y+z+y/z+x+1/x+y=1​

Answer 1

Answer:

Since

$x + y + z = 4$

Substitute

$\frac{1}{4} (x + y + z) = 1$

In first expression ' s numerators .

$\frac{1}{4} .\frac{x +( y + z)}{y + z} + \frac{1}{4} .\frac{y +( x + z)}{x + z} + \frac{1}{4} .\frac{(x +y )+ z}{x + y} = 1 \\ \\ \frac{x}{y + z} + \frac{y + z}{y + z} + \frac{y}{x + z} + \frac{x+ z}{x + z} + \frac{z}{x+ y} + \frac{x+ y}{x + y} = 4 \\ \\ \frac{x}{y + z} + 1 \frac{y }{x + z} + 1+ \frac{z}{x + y} + 1 = 4 \\ \\ \frac{x}{y + z} + \frac{y }{x + z} + \frac{z}{x + y} + 3 = 4 \\ \\ \frac{x}{y + z} + \frac{y }{x + z} + \frac{z}{x + y} = 4 - 3 = 1$