Question

Solve the equation. Check for extraneous solutions.
[(5/x)+(x+1/x+2)]=[(2x+9)/(x+2)]
Please show work. Thanks~

Answer 1

This?\[\frac{5}{x}+ \frac{x+1}{x+2}=\frac{2x+9}{x+2}\]

Answer 2

yes

Answer 3

On the left, find a common denominator and combine the terms:\[\frac{5(x+2)+x(x+1)}{x(x+2)}= \frac{2x+9}{x+2}\]Multiply both sides by x(x+2)\[5(x+2)+x(x+1) = x(2x+9)\]\[5x +10+x^{2}+x = 2x^{2}+9x\] Get all the terms on one side so it is equal to 0:\[x^{2}-3x-10=0\]Factor:\[(x-5)(x+2)=0\]So x is 5 or -2. However, if you use -2 in the original equation, it causes division-by-zero, so it is not a solution. So \[x=5\]

Answer 4

Thank you for being so helpful. Hopefully i will get this before the test. ='C