Question

What is the sum (Two-fifths x + StartFraction 5 over 8 EndFraction) + (one-fifth x minus one-fourth)?

Answer 1

Sum of
`((2)/(5)x+(5)/(8))+((1)/(5)x-(1)/(4))` is
`(3x)/(5)+(3)/(8)`

Explanation:

We need to find sum of (Two-fifths x + StartFraction 5 over 8 EndFraction) + (one-fifth x minus one-fourth)

Writing in mathematical form:

`((2)/(5)x+(5)/(8))+((1)/(5)x-(1)/(4))`

Solving

`(2)/(5)x+(5)/(8)+(1)/(5)x-(1)/(4)`

Combining like terms:

`=(2)/(5)x+(1)/(5)x+(5)/(8)-(1)/(4)\\Taking\,\,LCM\\=(2x+x)/(5)+(5-1*2)/(8)\\=(3x)/(5)+(3)/(8)`

So, sum of
`((2)/(5)x+(5)/(8))+((1)/(5)x-(1)/(4))` is
`(3x)/(5)+(3)/(8)`

Answer 2

`\frac24{x+15}{40}`

Explanation:

We want to find the sum of
`((2)/(5)x+(5)/(8))+((1)/(5)x-(1)/(4))`

We find the least common denominator to be 40

We collect LCM to obtain:

`(2x*8+5*5+8x-10)/(40)`

We simplify to get

`(16x+25+8x-10)/(40)`Simplify the numerator to obtain:

`(24x+15)/(40)`