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Lilit [14]
4 years ago
15

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

Mathematics
1 answer:
umka21 [38]4 years ago
5 0

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}

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