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Chapter 7: Problem 65

Explain how to find restrictions on the variable in a rational equation.

Short Answer

Expert verified
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.

Step by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{22 b+15}{12 b^{2}+52 b-9}+\frac{30 b-20}{12 b^{2}+52 b-9}-\frac{4-2 b}{12 b^{2}+52 b-9}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}}$$

Will help you prepare for the material covered in the next section. a. If \(y=\frac{k}{x},\) find the value of \(k\) using \(x=8\) and \(y=12\) b. Substitute the value for \(k\) into \(y=\frac{k}{x}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=3\)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{b}{a c+a d-b c-b d}-\frac{a}{a c+a d-b c-b d}$$
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