Question

Need help fast do not understand this one. Solve: (x+5) / (x+8)=1+(6) / (x+1) showing all work.

Answer 1

Answer:
`x=-(17)/(3)`

Explanation:

Given the equation
`((x+5))/((x+8))=1+(6)/((x+1))`, you need to make the addtition indicated on the right side of the equation:

`((x+5))/((x+8))=((x+1)+6)/((x+1))\\\\((x+5))/((x+8))=((x+7))/((x+1))`

Now, multiply both sides of the equation by (x+8) and (x+1):

`(x+1)(x+8)((x+5))/((x+8))=((x+7))/((x+1))(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)`

Now, apply Distributive property:

`x^2+5x+x+5=x^2+8x+7x+56`

Simplifying, you get:

`6x+5=15x+56`

Subtract 5 and 15x from both sides:

`6x+5-15x-5=15x+56-15x-5\\\\-9x=51`

Finally, divide both sidesby -9:

`(-9x)/(-9)=(51)/(-9)\\\\x=-(17)/(3)`