Question

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

Answer 1

Answer: $x=-\frac{17}{3}$

Step-by-step explanation:

Given the equation $\frac{(x+5)}{(x+8)}=1+\frac{6}{(x+1)}$, you need to make the addtition indicated on the right side of the equation:

$\frac{(x+5)}{(x+8)}=\frac{(x+1)+6}{(x+1)}\\\\\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}$

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

$(x+1)(x+8)\frac{(x+5)}{(x+8)}=\frac{(x+7)}{(x+1)}(x+1)(x+8)\\\\(x+1)(x+5)=(x+7)(x+8)$

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:

$\frac{-9x}{-9}=\frac{51}{-9}\\\\x=-\frac{17}{3}$