Question

Need help with this please show all work so I can really get the material

Answer 1

Step-by-step explanation

`(2)/(x^2+6x-7)+(3)/(x^2+8x+7)=(6)/(x^2-1)`

Factoring:

`(2)/((x+7)(x-1))+(3)/((x+7)(x+1))=(6)/((x+1)(x-1))`
`(2(x+7)(x+1)+3(x+7)(x-1))/((x+7)(x+7)(x+1)(x-1))=(6)/((x+1)(x-1))`
`(\left(x+1\right)\left(x-1\right)(2(x+7)(x+1)+3(x+7)(x-1)))/((x+7)(x+7)(x+1)(x-1))=6`
`(2(x+7)(x+1)+3(x+7)(x-1))/((x+7)(x+7))=6`
`\frac{(x+7){}(2(x+1)+3(x-1))}{(x+7)(x+7)}=6`
`(2(x+1)+3(x-1))/((x+7))=6`
`(2x+2+3x-3)/(x+7)=6`
`(5x-1)/(x+7)=6`
`5x-1=6(x+7)`
`5x-1=6x+42`
`5x-6x=42+1`
`-x=43`
`x=-43`

Answer

x=-43