Answer: [tex]x=-\frac{17}{3}[/tex]
Step-by-step explanation:
Given the equation [tex]\frac{(x+5)}{(x+8)}=1+\frac{6}{(x+1)}[/tex], you need to make the addtition indicated on the right side of the equation:
[tex]\frac{(x+5)}{(x+8)}=\frac{(x+1)+6}{(x+1)}\\\\\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}[/tex]
Now, multiply both sides of the equation by (x+8) and (x+1):
[tex](x+1)(x+8)\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)[/tex]
Now, apply Distributive property:
[tex]x^2+5x+x+5=x^2+8x+7x+56[/tex]
Simplifying, you get:
[tex]6x+5=15x+56[/tex]
Subtract 5 and 15x from both sides:
[tex]6x+5-15x-5=15x+56-15x-5\\\\-9x=51[/tex]
Finally, divide both sidesby -9:
[tex]\frac{-9x}{-9}=\frac{51}{-9}\\\\x=-\frac{17}{3}[/tex]
