3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15[tex] \frac{3}{4x+3} +\frac{21}{8x^2 +26x+15} [/tex]
factor the quadratic expression
⇒[tex] \frac{3}{4x+3} +\frac{21}{8x^2 +20x+6x+15}= \frac{3}{4x+3} +\frac{21}{4x(2x+5)+3(2x+5)} [/tex]
=[tex] \frac{3}{4x+3} +\frac{21}{(2x+5)(4x+3)} [/tex]
Find LCD , and make the denominators same by multiplying first expression by (2x+5) both in numerator and denominator
=[tex] \frac{3(2x+5)}{(4x+3)(2x+5)} +\frac{21}{(2x+5)(4x+3)} [/tex]
Simplify
=[tex] \frac{3(2x+5) +21}{(4x+3)(2x+5)} [/tex]
=[tex] \frac{6x+15 +21}{(4x+3)(2x+5)} [/tex]
=[tex] \frac{6x+36}{(4x+3)(2x+5)} [/tex]
Factor the numerator
=[tex] \frac{6(x+6)}{(4x+3)(2x+5)} [/tex]
Option D
