Question

What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15 ?

Answer 1

3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15$\frac{3}{4x+3} +\frac{21}{8x^2 +26x+15}$

factor the quadratic expression

⇒$\frac{3}{4x+3} +\frac{21}{8x^2 +20x+6x+15}= \frac{3}{4x+3} +\frac{21}{4x(2x+5)+3(2x+5)}$

=$\frac{3}{4x+3} +\frac{21}{(2x+5)(4x+3)}$

Find LCD , and make the denominators same by multiplying first expression by (2x+5) both in numerator and denominator

=$\frac{3(2x+5)}{(4x+3)(2x+5)} +\frac{21}{(2x+5)(4x+3)}$

Simplify

=$\frac{3(2x+5) +21}{(4x+3)(2x+5)}$

=$\frac{6x+15 +21}{(4x+3)(2x+5)}$

=$\frac{6x+36}{(4x+3)(2x+5)}$

Factor the numerator

=$\frac{6(x+6)}{(4x+3)(2x+5)}$

Option D

Answer 2

Answer:

-4x + 14

Step-by-step explanation: