Problem 66
Question
Simplify each complex rational expression. $$\frac{x-3}{x-\frac{3}{x-2}}$$
Step-by-Step Solution
Verified Answer
The simplified form of the complex rational expression is \(x^2 - 5x+ 6\).
1Step 1: Rewrite the Complex Fraction
Rewrite the complex fraction to remove the fraction in the denominator. The fraction \(x-3\) divided by \(\left(x-\frac{3}{x-2}\right)\) can be rewritten as \((x-3) \cdot \left(\frac{x-2}{x-3}\right)\)
2Step 2: Multiply
Now, we can multiply the two expressions that have been obtained after the previous step. You should obtain the fraction as \((x-3)\cdot(x-2)\). Make sure to distribute the multiplication to each term in the bracket. You will obtain \(x^2 - 5x+ 6\)
3Step 3: Final Simplification
The result obtained in step 2 is our simplified form of the original complex rational expression.
Other exercises in this chapter
Problem 66
Factor completely, or state that the polynomial is prime. $$5 x^{3}-45 x$$
View solution Problem 66
Write each number in decimal notation without the use of exponents. $$9.2 \times 10^{2}$$
View solution Problem 66
Perform the indicated operations. Indicate the degree of the resulting polynomial. $$\left(5 x^{4} y^{2}+6 x^{3} y-7 y\right)-\left(3 x^{4} y^{2}-5 x^{3} y-6 y+
View solution Problem 66
Evaluate each expression in Exercises \(55-66,\) or indicate that the root is not a real number. $$\sqrt[6]{\frac{1}{64}}$$
View solution