Question

Given that $\frac{x^2+6x+9}{x+3}=7$, what is $x$?

• A. $-4$
• B. $3$
• C. $-3$
• D. $2$

Answer 1

The correct option is C $-3$

Cross-multiply, simplify and factor to solve:

$\frac{x^2+6x+9}{x+3}=7$

$x^2+6x+9=7x+21$

$x^2-x-12=0$

$(x+3)(x-4)=0$

$x+3=0$ or $x-4=0$

$x=-3$ or $x=4$

Discard $-3$ as a value for $x$ since this value would make the denominator $0$; thus the fraction would be undefined.