Equivalent Expressions 3 — Advanced Math

Questions in this quiz (7)

1. Which of the following expressions is equivalent to $$\frac{x^2+4x-12}{x+6}$$?

   • $$x-2$$
   • $$x-2-\frac{24}{x+6}$$
   • $$x+10-\frac{48}{x+6}$$
   • $$x+10+\frac{48}{x+6}$$

2. Which of the following is equivalent to $$\frac{x^2+y^2-z^2+2xy}{x^2+z^2-y^2+2xz}$$?

   • $$\frac{x+y-z}{x+z-y}$$
   • $$\frac{x+z-y}{x+y-z}$$
   • $$-1$$
   • $$1$$

3. The expression $$x^4-10x^2-24$$ can be written as $$(x^2+b)(x+a)(x-a)$$, where $$a$$ and $$b$$ are constants. What is the value of $$ab$$?

   • $$2$$
   • $$2\sqrt{3}$$
   • $$4\sqrt{3}$$
   • $$4$$

4. If $$m$$ and $$n$$ are positive numbers such that $$m$$ > $$n$$, which of the following is equivalent to $$\frac{\sqrt{(m-n)^7}}{\sqrt{(m-n)^{-3}}}$$?

   • $$m-n$$
   • $$(m-n)^2$$
   • $$(m-n)^4$$
   • $$(m-n)^5$$

5. If $$c-w$$ is a factor of the expression $$-w^2+\frac{1}{17}pc^2$$, where $$p$$ and $$c$$ are constants and $$c$$ > $$0$$, what is the value of $$p$$?

   • $$-17$$
   • $$-\frac{1}{17}$$
   • $$\frac{1}{17}$$
   • $$17$$

6. $$\frac{5}{x-2}+\frac{3}{x+4}=\frac{ax+b}{(x-2)(x+4)}$$The equation above is true for all $$x$$ > $$2$$, where $$a$$ and $$b$$ are positive constants. What is the value of $$ab$$?

   • $$8$$
   • $$14$$
   • $$96$$
   • $$112$$

7. If $$t=a-b$$, which of the following is equivalent to the expression $$t^2-a^2+2ab-b^2$$?

   • $$-a-b$$
   • $$0$$
   • $$-a^2+ab-b^2$$
   • $$-1$$