Question

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

A. 6(2x+5) / (2x-5)(4x+3)
B. 6/(4x+3)
C. 6(x+6)/ (2x-5)(4x+3)
D. 6(x+6)/ (2x+5)(4x+3)

Answer 1

-4x + 14

Explanation:

Answer 2

3 over 4x plus 3 + 21 over 8 x squared plus 26x plus 15
`(3)/(4x+3) +(21)/(8x^2 +26x+15)`

factor the quadratic expression

⇒
`(3)/(4x+3) +(21)/(8x^2 +20x+6x+15)= (3)/(4x+3) +(21)/(4x(2x+5)+3(2x+5))`

=
`(3)/(4x+3) +(21)/((2x+5)(4x+3))`

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

=
`(3(2x+5))/((4x+3)(2x+5)) +(21)/((2x+5)(4x+3))`

Simplify

=
`(3(2x+5) +21)/((4x+3)(2x+5))`

=
`(6x+15 +21)/((4x+3)(2x+5))`

=
`(6x+36)/((4x+3)(2x+5))`

Factor the numerator

=
`(6(x+6))/((4x+3)(2x+5))`

Option D