`a)(5x+5y)/A=(5x²-5y²)/(2y-2x)`
`→A=[(5x+5y)(2y-2x)]/(5x²-5y²)`
`=[5(x+y).2(y-x)]/[5(x²-y²)]`
`=[10(x+y)(y-x)]/[5(x²-y²)]`
`=[-10(x+y)(x-y)]/[5(x+y)(x-y)]`
`=-2`
`b)(x³+x²)/(x²-1)=B/(x-1)`
`→B=[(x³+x²)(x-1)]/(x²-1)`
`=[x²(x+1)(x-1)]/[(x+1)(x-1)]`
`=x²`
`c)(-x²+2xy-y²)/(x+y)=C/(y²-x²)`
`→C=[(-x²+2xy-y²)(y²-x²)]/(x+y)`
`=[-(x²-2xy+y²)(y²-x²)]/(x+y)`
`=[(x²-2xy+y²)(x²-y²)]/(x+y)`
`=[(x-y)²(x+y)(x-y)]/(x+y)`
`=[(x-y)³(x+y)]/(x+y)`
`=(x-y)³`
`=x³-3x²y+3xy²-y³`
`d)(x²+8)/(2x-1)=(3x³+24x)/D`
`→D=[(2x-1)(3x³+24x)]/(x²+8)`
`=[3x(2x-1)(x²+8)]/(x²+8)`
`=3x(2x-1)`
`=6x²-3x`
`e)E/(x-y)=(3x²-3xy)/[3(y-x)²]`
`→E=[(x-y)(3x²-3xy)]/[3(y-x)²]`
`=[3x(x-y)(x-y)]/[3(x-y)²]`
`=[3x(x-y)²]/[3(x-y)²]`
`=x`
