To simplify this, you need a common denominator.
Since 4x + 4y = 4(x + y), a common denominator is: 4(x + y)(x - y)
Solving: [ 3/(4(x + y)) ] · [ (x - y)/(x - y) ] + [ 1/(x - y) ] · [ 4(x + y) ]/[ 4·(x + y) ]
= [ 3(x - y) ] / [ 4(x + y)(x - y) ] + [ 1·4(x + y) ] / [ 4(x + y)(x - y) ]
= [ 3(x - y) + 4(x + y) ] / [ 4(x + y)(x - y) ]
= [ 3x - 3y + 4x + 4y ] / [ 4(x + y)(x - y) ]
= [ 7x + y ] / [ 4(x + y)(x - y) ]
To simplify this, you need a common denominator.
Since 4x + 4y = 4(x + y), a common denominator is: 4(x + y)(x - y)
Solving: [ 3/(4(x + y)) ] · [ (x - y)/(x - y) ] + [ 1/(x - y) ] · [ 4(x + y) ]/[ 4·(x + y) ]
= [ 3(x - y) ] / [ 4(x + y)(x - y) ] + [ 1·4(x + y) ] / [ 4(x + y)(x - y) ]
= [ 3(x - y) + 4(x + y) ] / [ 4(x + y)(x - y) ]
= [ 3x - 3y + 4x + 4y ] / [ 4(x + y)(x - y) ]
= [ 7x + y ] / [ 4(x + y)(x - y) ]