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$\\dfrac{2(x+1)}{x+5}=1-\\dfrac{1}{x+5}$

What is the solution to the equation above?

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$\\dfrac{2(x+1)}{x+5}=1-\\dfrac{1}{x+5}$

What is the solution to the equation above?

","comment":{"@type":"Comment","text":"

Choice B is correct. Since $\\dfrac{x+5}{x+5}$ is equivalent to 1, the right-hand side of the given equation can be rewritten as $\\dfrac{x+5}{x+5}-\\dfrac{1}{x+5}$, or $\\dfrac{x+4}{x+5}$. Since the left- and right-hand sides of the equation $\\dfrac{2(x+1)}{x+5}=\\dfrac{x+4}{x+5}$ have the same denominator, it follows that \$2(x+1)=x+4\$. Applying the distributive property of multiplication to the expression \$2(x+1)\$ yields \$2(x)+2(1)\$, or \$2x+2\$. Therefore, $2x+2=x+4$. Subtracting $x$ and $2$ from both sides of this equation yields $x=2$.

Choices A, C, and D are incorrect. If $x=0$, then $\\dfrac{2(0+1)}{0+5}=1-\\dfrac{1}{0+5}$. This can be rewritten as $\\dfrac{2}{5}= \\dfrac{4}{5}$, which is a false statement. Therefore, $0$ isn’t a solution to the given equation. Substituting $3$ and $5$ into the given equation yields similarly false statements.

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$\\dfrac{2(x+1)}{x+5}=1-\\dfrac{1}{x+5}$

What is the solution to the equation above?

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$\dfrac{2(x+1)}{x+5}=1-\dfrac{1}{x+5}$

What is the solution to the equation above?