What is the simplified form of 3 over 4x plus - id3432875082, fannyrivera321

Ответ:

emcarrell

12.03.2022

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

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