DSAT extra practice Ch4 Lv2

$$\frac{x^2+5x+1}{x+3}$$Which of the following expressions is equivalent to the given expression?

If [math]m=\dfrac{1}{2x-3}[/math], what is the value of [math]m+m^{-1}[/math]?

$$\frac{x^2(x+1)+2x+2}{x+1}$$If [math]x\neq-1[/math], which of the following expressions is equivalent to the given expression?

If [math]x=\sqrt[3]{17}[/math], what is the value of [math]x^{-3}[/math]?

$$(\sqrt{5})^x=25^{\frac{1}{3}}$$What is the solution to the equation above?

If [math]\sqrt[a]{3^b}=\sqrt{3}[/math], which of the following statements is true?

Which of the following numbers is negative?

$$f(x)=\dfrac{x-1}{(x^2-1)(x+2)}$$What is the domain of [math]f(x)[/math]?

$$f(x)=-2+\frac{5}{x+3}$$Which of the following values is closed to the number [math]f(100000)[/math]?

$$f(x)=2x^2+7x+3$$If [math]g(x)=\dfrac{1}{f(x)}[/math], how many possible values of [math]n[/math] such that [math]g(n)[/math] is undefined?

In order to drain a swimming pool, a worker prepared two pumps. Alone, it takes pump A [math]x[/math] hours to drain the pool and it take pump B 4 more hours than pump A to drain the pool. If two pumps work together, it will take 12 hours to drain the pool. Which of the following equation can help us to find the value of [math]x[/math]?

A bottle of plum drink is 500 ml and contains 30\% plum juice. If Mia poured half a bottle of plum drink and [math]x[/math] ml of plum juice into his mug, the concentration of plum juice in his drink becomes 50\%. Which of the following equations best represent this situation?

$$(x+1)^{-2}=-2(x+1)$$Which of the following numbers is a solution to the equation above?

Let [math]x[/math] and [math]y[/math] be two real numbers. If [math]x+y=3[/math] and [math]\dfrac{1}{x}+\dfrac{1}{y}=6[/math], what is the value of [math]xy[/math]?

$$\frac{9}{\sqrt{11}-2}$$If the expression above can be written as [math]a+b\sqrt{11}[/math] where [math]a[/math] and [math]b[/math] are rational numbers, what is the value of [math]a[/math]?

If [math]x=5\sqrt{3}[/math], what is the value of [math]\sqrt{x}[/math]?

If [math]4-2\sqrt{3}[/math] can be written as [math](a-b\sqrt{3})^2[/math] where [math]a[/math] and [math]b[/math] are positive integers, what is the value of [math]a-b[/math]?

$$\frac{\sqrt{x}-\sqrt{x-1}}{\sqrt{x}+\sqrt{x-1}}$$If the expression above can be written as [math]ax+b+c\sqrt{x(x-1)}[/math] where [math]a, b[/math], and [math]c[/math] are integers, what is the value of [math]b[/math]?

$$\sqrt{x+1}=\dfrac{8}{x+1}$$What is the solution to the equation above?

$$\sqrt{2x+1}+x=7$$What is the solution set of the equation above?

How many solutions does the equation [math]\sqrt{|x+3|}=7[/math] have?

$$f(x)=\sqrt{x+2}$$$$g(x)=-2x-1$$What is the [math]x[/math]-coordinate of the intersection of [math]f(x)[/math] and [math]g(x)[/math]?

$$\frac{1}{\sqrt{x}-2}=6$$What is the solution to the equation above?