Rationalize this equation (7/(x-8)=(x+1)/(x-8)+(x+1)/(x^2-8x))

To rationalize the given equation:

\[
\frac{7}{x - 8} = \frac{x + 1}{x - 8} + \frac{x + 1}{x^2 - 8x}
\]

we want to eliminate the fractions by finding a common denominator and expressing all terms with that denominator.

### Step 1: Identify Common Denominator

The denominators are \(x - 8\) and \(x^2 - 8x\). Notice that:

\[
x^2 - 8x = x(x - 8)
\]

So, the common denominator for all terms is \(x(x - 8)\).

### Step 2: Rewrite Each Fraction with the Common Denominator

Rewrite each fraction so that they all have the common denominator \(x(x - 8)\):

1. \(\frac{7}{x - 8}\) becomes \(\frac{7x}{x(x - 8)}\)
2. \(\frac{x + 1}{x - 8}\) becomes \(\frac{(x + 1)x}{x(x - 8)}\)
3. \(\frac{x + 1}{x^2 - 8x}\) remains \(\frac{x + 1}{x(x - 8)}\)

### Step 3: Substitute and Simplify the Equation

Substitute these expressions into the equation:

\[
\frac{7x}{x(x - 8)} = \frac{(x + 1)x}{x(x - 8)} + \frac{x + 1}{x(x - 8)}
\]

Combine the fractions on the right-hand side:

\[
\frac{7x}{x(x - 8

Learn how to rationalize the equation 7/(x-8) = (x+1)/(x-8) + (x+1)/(x^2-8x) with a step-by-step solution. This problem involves rational equations and finding common denominators. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation