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Hello, I need help solving this practice problems with showing appropriate work for each step. Thank you!

Hello, I need help solving this practice problems with showing appropriate work for-example-1

1 Answer

4 votes

Answer:

Computing the sum of fractions on the left side of the equation, we get:


(x(x+5)+3(x+4))/((x+4)(x+5))=(x+2)/(x^2+9x+20).

Now, notice that:


x^2+9x+20=(x+4)(x+5).

Therefore, we can rewrite the equation as:


(x(x+5)+3(x+4))/((x+4)(x+5))=(x+2)/((x+4)(x+5)).

The above result implies that:


x(x+5)+3(x+4)=x+2.

Simplifying the above equation, we get:


\begin{gathered} x^2+5x+3x+12=x+2, \\ x^2+8x+12=x+2. \end{gathered}

Subtracting x+2, we get:


x^2+7x+10=0.

Notice that:


x^2+7x+10=(x+2)(x+5).

Therefore,


x=-2,\text{ }

because x≠-5, otherwise we could not have a denominator of x+5.

Answer:


x=2.

User Oenotria
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