找到你今天要练的题。

Which expression is equivalent to\( \frac{y+13}{x-10}+\frac{y\left(x-10\right)}{x^2y-10xy} \) ?

\( \frac{2}{c}-\frac{7}{d}=5 \) 
The given equation relates the variables c and d, where c and d are greater than 1. Which equation correctly expresses d in terms of c?

The function g is defined as \( g\left(x\right)=\frac{2x-6}{\left(x+13\right)\left(x-8\right)} \) . If \( g\left(a+7\right)=0 \), where a is a constant, what is the value of a?

\( \frac{32}{p}=\frac{32}{q}-\frac{32}{r}-\frac{32}{s} \) 
The given equation relates the positive variables p, q, r, and s. Which of the following is equivalent to q?

If \( \frac{72}{x}=6x \), what is the value of \( 6x^2 \) ?

\( \frac{\left(x-8\right)\left(x-16\right)}{x-7}=0 \) 
What is the sum of the solutions to the given equation?

The function \( f \) is defined by\( f\left(x\right)=\frac{x^2+ax+b}{2x+c} \) , where a, b, and c are constants. The graph of the function \( f \) in the xy-plane, where \( y=f\left(x\right) \), does not intersect the line \( x=4 \) . If \( f(5)=f(6)=0 \). What is the value of \( a+b+c \) ?

\( \frac{46}{p}=\frac{46}{q}-\frac{46}{r}-\frac{46}{s} \) 
The given equation relates the positive variables p, q, r, and s. Which of the following is equivalent to q?

In the xy-plane, the graph of function \( f \), where \( y=f(x) \) , has exactly 8 x-intercepts. One of these x-intercepts is (17, 0). The rational function g is defined by \( g(x)=\frac{f(x)}{x-17} \). In the xy-plane, how many x-intercepts does the graph of \( y=g(x) \)  have?

\( \frac{\left(x-7\right)\left(x-9\right)}{x-4}=0 \) 
What is the sum of the solutions to the given equation?

\( \frac{x+1}{5x^2}=\frac{k}{x} \) 
In the given equation, k is a constant. The solution to the given equation is \( \frac{1}{224} \). What is the value of k ?

The table shows three values of \( x \) and their corresponding values of \( f(x) \), where \( f\left(x\right)=\frac{kx+63}{x+3} \) and \( k \) is a constant. What is the value of \( k \)?