Focus on $x^2 - 4x - 21$. Look for two numbers that multiply to $-21$ and add up to $-4$ so you can factor this quadratic expression.

After you factor the numerator, see if any factor cancels with the denominator. This will turn the equation into a much simpler linear equation to solve.

Once you find a value for $x$, substitute it back into the original equation to verify that the left side really equals $-3$ and that the denominator is not $0$.

In Desmos, type y = (x^2 - 4x - 21)/(x - 7) on one line and y = -3 on another line. These are the left and right sides of the equation as graphs.

Look for the point where the curve $y = (x^2 - 4x - 21)/(x - 7)$ intersects the horizontal line $y = -3$. Tap or click on that intersection point; Desmos will display its coordinates. The x-coordinate of this intersection is the solution to the equation.

Make sure that the x-value from the intersection is not $7$ (since $x = 7$ would make the denominator $0$ and is not allowed). You can also create a table for the first function and plug in that x-value to confirm that the corresponding y-value is $-3$.

The denominator is $x-7$, so $x$ cannot be $7$ (this would make the denominator $0$, which is undefined).

Now factor the numerator $x^2 - 4x - 21$. Look for two numbers that multiply to $-21$ and add to $-4$. Those numbers are $-7$ and $3$, so:

Rewrite the left side of the equation using the factored form:

For $x \neq 7$, you can cancel $(x - 7)$ from the numerator and denominator:

So the original equation becomes:

Solve $x + 3 = -3$ by subtracting $3$ from both sides:

This value does not make the denominator $x - 7$ equal to $0$, so it is allowed.

Check in the original equation:

• Numerator: $(-6)^2 - 4(-6) - 21 = 36 + 24 - 21 = 39$
• Denominator: $-6 - 7 = -13$
• Left side: $\dfrac{39}{-13} = -3$, which matches the right side.

Therefore, the value of $x$ that satisfies the equation is $-6$.