Đáp án:
`a)A=-2`
`b)B=x²`
`c)C=(x-y)³`
`d)D=3x(2x-1)`
`e)E=x`
Giải thích các bước giải:
`a)(5x+5y)/A=(5x²-5y²)/(2y-2x)`
`⇒A=[(5x+5y)(2y-2x)]/(5x²-5y²)`
`⇒A=[10(x+y)(y-x)]/[5(x²-y²)]`
`⇒A=[-10(x+y)(x-y)]/[5(x+y)(x-y)]`
`⇒A=-2`
Vậy `A=-2`
`b)(x³+x²)/(x²-1)=B/(x-1)`
`⇒B=[(x³+x²)(x-1)]/(x²-1)`
`⇒B=[x²(x+1)(x-1)]/[(x+1)(x-1)]`
`⇒B=x²`
Vậy `B=x²`
`c)(-x²+2xy-y²)/(x+y)=C/(y²-x²)`
`⇒C=[(-x²+2xy-y²)(y²-x²)]/(x+y)`
`⇒C=[(x²-2xy+y²)(x²-y²)]/(x+y)`
`⇒C=[(x-y)²(x+y)(x-y)]/(x+y)`
`⇒C=[(x-y)³(x+y)]/(x+y)`
`⇒C=(x-y)³`
Vậy `C=(x-y)³`
`d)(x²+8)/(2x-1)=(3x³+24x)/D`
`⇒D=[(2x-1)(3x³+24x)]/(x²+8)`
`⇒D=[3x(2x-1)(x²+8)]/(x²+8)`
`⇒D=3x(2x-1)`
Vậy `D=3x(2x-1)`
`e)E/(x-y)=(3x²-3xy)/[3(y-x)²]`
`⇒E=[(x-y)(3x²-3xy)]/[3(y-x)²]`
`⇒E=[3x(x-y)(x-y)]/[3(x-y)²]`
`⇒E=[3x(x-y)²]/[3(x-y)²]`
`⇒E=x`
Vậy `E=x`
