Problem 65
Question
Explain how to find restrictions on the variable in a rational equation.
Step-by-Step Solution
Verified Answer
To find the restrictions on the variables in a rational equation, identify the equation, set each fraction's denominator equal to zero, and solve for the variable.
1Step 1: Identify the Rational Equation
To find the restrictions on the variables in a rational equation, the first step is to identify the rational equation. A rational equation is an equation in the form \( \frac{a}{b} = c \), where a and b are polynomials, and c is a constant.
2Step 2: Set the Denominator Equal to Zero
The next step is to set the denominator equal to zero. For our rational equation \( \frac{a}{b} = c \), we set b equal to zero, i.e., \( b = 0 \) and solve for the variable. This will give the values of the variable for which the denominator becomes 0.
3Step 3: Solve for the Variable
After setting the denominator equal to zero, solve the equation for the variable. The solutions to this equation are the restrictions on the variable.
Other exercises in this chapter
Problem 65
Add or subtract as indicated. Simplify the result, if possible. $$4+\frac{1}{x-3}$$
View solution Problem 65
Perform the indicated operation or operations. $$\left(\frac{y-2}{y^{2}-9 y+18} \cdot \frac{y^{2}-4 y-12}{y+2}\right) \div \frac{y^{2}-4}{y^{2}+5 y+6}$$
View solution Problem 66
perform the indicated operation or operations. Simplify the result, if possible. $$\frac{22 b+15}{12 b^{2}+52 b-9}+\frac{30 b-20}{12 b^{2}+52 b-9}-\frac{4-2 b}{
View solution Problem 66
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9 x-15}{5-3 x}$$
View solution