DSAT extra practice Ch4 Lv1

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

$$\dfrac{x-1}{x+2}\cdot\dfrac{x-1}{x-2}$$Which of the following expressions is equivalent to the given expression?

$$\frac{3}{2-\frac{4}{x}}$$Which of the following expressions is equivalent to the given expression?

$$\frac{4}{x+2}+\frac{1}{x-5}=\frac{ax+b}{(x+2)(x-5)}$$If the given equation is an identity, what is the value of [math]a+b[/math]?

$$m=\frac{(x+3)(x-1)}{x(x-1)}$$What is the value of [math]m[/math] if [math]x=1[/math]?

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

If [math]x^{\frac{2}{3}}=9[/math], which of the following values could be [math]x[/math]?

If [math]\sqrt[7]{64}=4^a[/math], what is the value of [math]a[/math]?

If [math]x=-6^{\frac{3}{5}}[/math], which of the following numbers is an integer?

$$\sqrt[n]{16}=2^n$$What is the solution to the equation above?

$$f(x)=3+\frac{5}{x-4}$$Which of the following equations is a horizontal asymptote of [math]f(x)[/math]?

$$f(x)=-3+\dfrac{1}{x+5}$$What is the [math]x[/math]-intercept of [math]f(x)[/math]?

$$f(x)=-1+\frac{2}{3-x}$$What is the range of [math]f(x)[/math]?

Which of the following rational functions has no vertical asymptotes?

$$\frac{2}{x+1}=\frac{x+1}{18}$$Which of the following numbers is a solution to the equation above?

$$\frac{4}{x+2}+\frac{x}{x-2}=1$$What is the solution to the given equation?

Consider a fraction [math]\dfrac{3}{17}[/math]. If we add [math]x[/math] to both the denominator and numerator, then this fraction will be equal to one half. What is the value of [math]x[/math]?

$$\frac{3}{x-2}+\frac{2}{x+3}=\frac{4}{x+3}$$What is the solution to the given equation?

$$\sqrt[3]{-8x^4y^7}$$If the expression above can be written as [math]ax^by^c\sqrt[3]{xy}[/math] where [math]a, b[/math], and [math]c[/math] are integers, what is the value of [math]a+b+c[/math]?

$$\frac{3+\sqrt{3}}{\sqrt{3}}$$If the expression above can be written as [math]a+b\sqrt{3}[/math] where [math]a[/math] and [math]b[/math] are integers, what is the value of [math]a+b[/math]?

$$\dfrac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}$$Which of the following expression is equivalent to the expression above?

$$\frac{3}{\sqrt{x-2}}$$Which of the following expression is equivalent to the expression above?

$$\sqrt{x}=x-1$$If [math]x=\dfrac{a-b\sqrt{5}}{2}[/math] is a solution to the equation where [math]a[/math] and [math]b[/math] are positive integer, what is the value of [math]b[/math]?

$$\sqrt{x^2-6x+9}=3$$How many solutions does the equation have?