Question

If x, y, a and b are greater than zero and x/y lessthanorequalto a/b, prove that x+a/y+b lessthanorequalto a/b

Answer 1

Explanation:

Given x,y,a&b are greater than zero

also
`(x)/(y)`
`\leq`
`(a)/(b)`

since x,y,a&b are greater than zero therefore we can cross multiply them without changing the inequality

therefore

`(x)/(a)`
`\leq`
`(y)/(b)`

adding 1 on both sides we get

`(x)/(a)`+1
`\leq`
`(y)/(b)`+1

`(x+a)/(a)`
`\leq`
`(y+b)/(b)`

rearranging

`(x+a)/(y+b)`
`\leq`
`(a)/(b)`