Chapter 11.4, Problem 4MCQ

To determine

Simplify $\frac{2x^2+13+15}{2x+10}$

Answer to Problem 4MCQ

  $\frac{2x+3}{2}$

Explanation of Solution

Given:

  $\frac{2x^2+13+15}{2x+10}$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to simplify expression, first factor out neminator as shown below,

  $\begin{array}{c}\frac{2x^2+13+15}{2x+10}=\frac{2x^2+13+15}{2\left(x+5\right)}\\ =\frac{\left(2x+3\right)\left(x+5\right)}{2\left(x+5\right)}\\ =\frac{2x+3}{2}\end{array}$

Thus, the solution is $\frac{2x+3}{2}$.