$\frac{x - 9}{x + 4} = 3$ $(x-9)/(x+4)=3$ ?

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$\frac{x - 9}{x + 4} = 3$ $(x-9)/(x+4)=3$ ?

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Answer 1 · 2018-04-26T17:53:30

$x = - \frac{21}{2}$ $x=-21/2$

Explanation:

$\frac{x - 9}{x + 4} = 3$ $(x-9)/(x+4)=3$ $/ \cdot (x + 4)$ $/*(x+4)$ to get rid of the fraction

$x - 9 = 3 \cdot (x + 4)$ $x-9=3*(x+4)$

$x - 9 = 3 x + 12$ $x-9=3x+12$

$x - 3 x = 12 + 9$ $x-3x=12+9$

$- 2 x = 21$ $-2x=21$ $/ \cdot (- 1)$ $/*(-1)$

$2 x = - 21$ $2x=-21$

$x = - \frac{21}{2}$ $x=-21/2$

Answer 2 · 2018-04-26T17:57:44

$x = - \frac{21}{2}$ $x = -21/2$

Explanation:

We must begin by adding the domain restriction $x \neq - 4$ $x!=-4$ because this would cause division by 0:

$\frac{x - 9}{x + 4} = 3, x \neq - 4$ $(x-9)/(x+4)=3, x !=-4$

Now that we have assured that we are not inadvertently multiplying by 0, we can eliminate the denominator by multiplying both sides by $(x + 4)$ $(x+4)$ :

$x - 9 = 3 (x + 4), x \neq - 4$ $x-9=3(x+4), x !=-4$

Use the distributive property:

$x - 9 = 3 x + 12, x \neq - 4$ $x-9=3x+12, x !=-4$

Add $9 - 3 x$ $9-3x$ to both sides:

$- 2 x = 21, x \neq - 4$ $-2x = 21, x!=-4$

We can drop the domain restriction because it is obvious that the solution will not violate it:

$- 2 x = 21$ $-2x = 21$

Multiply both sides by $- \frac{1}{2}$ $-1/2$ :

$x = - \frac{21}{2}$ $x = -21/2$

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$\frac{x - 9}{x + 4} = 3$ $(x-9)/(x+4)=3$ ?

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2 Answers

Explanation:

Explanation:

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