Final answer:
To simplify the expression (10x² +14x)/(5x+7), we use polynomial long division to obtain the simplified expression 2x - 14/(5x+7).
Step-by-step explanation:
To simplify the expression (10x² +14x)/(5x+7), we can use the method of polynomial long division.
Step 1: Divide the first term of the numerator by the first term of the denominator. This gives us 10x² ÷ 5x = 2x.
Step 2: Multiply the result of step 1 by the denominator, and subtract from the numerator. This gives us (10x² + 14x) - (2x)(5x+7) = 14x - 14x - 14 = -14.
Step 3: Write the simplified expression as the quotient plus the remaining constant term over the denominator. Therefore, the simplified expression is 2x - 14/(5x+7).