Problem 37
Question
Add or subtract as indicated. $$\frac{4 x-10}{x-2}-\frac{x-4}{x-2}$$
Step-by-Step Solution
Verified Answer
The simplified form of \( \frac{4 x-10}{x-2}-\frac{x-4}{x-2} \) is \(\frac{3x - 6}{x - 2}\)
1Step 1: Identify Common Denominator
Observe that the denominators of both fractions are identical which allows us to proceed to the next step. The denominator is \(x-2\) for both fractions.
2Step 2: Combine Numerators
As the fractions already have a common denominator, the subtraction operation is performed in the numerators. The new numerator becomes the result of \( (4x-10) - (x-4)\).
3Step 3: Simplify Numerator
Now focus on simplifying the numerator by combining like terms. After subtracting, the numerator simplifies to \(4x - x -10 +4\). Simplify this further to get \(3x - 6\).
4Step 4: Write Final Answer
Insert the simplified numerator back into the fraction. The final answer to the problem is \(\frac{3x - 6}{x - 2}\).
Other exercises in this chapter
Problem 37
Find each product. $$\left(4 x^{2}+5 x\right)\left(4 x^{2}-5 x\right)$$
View solution Problem 37
Factor each trinomial, or state that the trinomial is prime. $$ 6 x^{2}-5 x y-6 y^{2} $$
View solution Problem 37
List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, i. real numbers. \(\
View solution Problem 38
Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$
View solution