Rational equation solving (SAT) Practice Questions (Grade 9)

Question 1easy

If $\dfrac{(x+7)(x+1)}{x+7} = -2$ and $x \neq -7$ , what is the value of $x$ ?

For $x \neq -7$ , cancel $x+7$ to get $x+1 = -2$ , so $x = -3$ .

Question 2easy

If $\dfrac{(x-3)(x+5)}{x-3} = 12$ and $x \neq 3$ , what is the value of $x$ ?

For $x \neq 3$ , cancel $x-3$ to get $x+5 = 12$ , so $x = 7$ .

Question 3medium

If $\dfrac{(x+2)(x-8)}{x+2} = 5$ and $x \neq -2$ , what is the value of $x$ ?

For $x \neq -2$ , cancel $x+2$ to get $x-8 = 5$ , so $x = 13$ .

Question 4medium

What is the value of $x$ if $\dfrac{x^2 - 25}{x + 5} = 2$ and $x \neq -5$ ?

Factor the numerator: $x^2 - 25 = (x-5)(x+5)$ . For $x \neq -5$ , cancel $x+5$ to get $x-5 = 2$ , so $x = 7$ .

Question 5medium

What is the value of $x$ if $\dfrac{x^2 - 16}{x - 4} = 9$ and $x \neq 4$ ?

Factor the numerator: $x^2 - 16 = (x-4)(x+4)$ . For $x \neq 4$ , cancel $x-4$ to get $x+4 = 9$ , so $x = 5$ .

Question 6medium

What is the value of $x$ if $\dfrac{x^2 - 49}{x - 7} = 6$ and $x \neq 7$ ?

Factor the numerator: $x^2 - 49 = (x-7)(x+7)$ . For $x \neq 7$ , cancel $x-7$ to get $x+7 = 6$ , so $x = -1$ .

Question 7medium

What is the value of $x$ if $\dfrac{x^2 + 6x + 9}{x + 3} = 4$ and $x \neq -3$ ?

Factor the numerator as a perfect square: $x^2 + 6x + 9 = (x+3)^2$ . For $x \neq -3$ , cancel $x+3$ to get $x+3 = 4$ , so $x = 1$ .

Question 8medium

What is the value of $x$ if $\dfrac{x^2 + 10x + 25}{x + 5} = 3$ and $x \neq -5$ ?

Factor the numerator as a perfect square: $x^2 + 10x + 25 = (x+5)^2$ . For $x \neq -5$ , cancel $x+5$ to get $x+5 = 3$ , so $x = -2$ .

Rational equation solving (SAT) practice