DSAT extra practice Ch4 Lv3

$$\frac{ax+b}{x^2+x+1}-\frac{c}{x+1}$$If the expression above can be written as [math]\dfrac{P(x)}{(x^2+x+1)(x+1)}[/math] where [math]a, b,[/math] and [math]c[/math] are nonzero constants and [math]P(x)[/math] is a polynomial function, which of the following statements must be false?

$$\sqrt{x}\sqrt[3]{x}\sqrt[4]{x}=7$$what is the solution to the equation above?

$$n=\sqrt{3\sqrt{3}}$$Which of the following values is equal to [math]n[/math]?

$$f(x)=\frac{-x}{x^2+12x+c}$$If [math]f(x)[/math] has no vertical asymptotes, what is the condition of constant [math]c[/math]?

The figure above shows the graph of function [math]f(x)[/math] If we translate [math]f(x)[/math] 3 units to the right and 4 units down, which of the following equations could be new [math]f(x)[/math]?

The figure above shows the graph of [math]f(x)=a+\dfrac{b}{x+c}[/math] where [math]a, b[/math], and [math]c[/math] are constants, what is the value of [math]a+b+c[/math]?

$$\frac{3}{x+a}+\frac{1}{x-3}=\frac{6}{x}$$If [math]x=-4.5[/math] is a solution to the equation above, what is the value of constant [math]a[/math]?

$$\frac{3x+5}{2x+7}=\frac{2x+7}{3x+5}$$If [math]x=-\dfrac{p}{q}[/math] is a solution to the equation above where [math]p[/math] and [math]q[/math] are positive coprime integer (i.e. the greatest common factor is 1), what is the value of [math]p+q[/math]?

If [math]\sqrt{p+q}=5[/math] and [math]\sqrt{p-q}=3[/math], which of the following statements is true?

$$f(x)=\sqrt{x^2-1}$$$$g(x)=\sqrt{x-1}\sqrt{x+1}$$Which of the following statements is true?

$$f(x)=x$$$$g(x)=-1+2\sqrt{x+a}$$If [math]f(x)[/math] and [math]g(x)[/math] has only one intersection, what is the value of [math]a[/math]?

Which of the following number is a solution to equation [math](x+1)-\sqrt{x+1}=6[/math]?

$$\sqrt{4x+a}=x+7$$The radical equation above has two solutions. If [math]a[/math] is an integer, what is the minimum possible of [math]a[/math]?