Answer:
9(x + 3)
Step-by-step explanation:
[tex] \dfrac{2x^2 + x - 15}{2x^2 - 11x - 21} \times (6x + 9) \div \dfrac{2x - 5}{3x - 21} = [/tex]
Change division into multiplication by reciprocal.
[tex] = \dfrac{2x^2 + x - 15}{2x^2 - 11x - 21} \times (6x + 9) \times \dfrac{3x - 21}{2x - 5} [/tex]
Factor every polynomial.
[tex] = \dfrac{(2x - 5)(x + 3)}{(x - 7)(2x + 3)} \times 3(2x + 3) \times \dfrac{3(x - 7)}{2x - 5} [/tex]
Combine all factors into a single fraction.
[tex] = \dfrac{9(2x - 5)(x + 3)(2x + 3)(x - 7)}{(x - 7)(2x + 3)(2x - 5)} [/tex]
Rearrange terms and separate fractions to see what simplifies.
[tex] = \dfrac{9(x + 3)}{1} \times \dfrac{2x - 5}{2x - 5} \times \dfrac{2x + 3}{2x + 3} \times \dfrac{x - 7}{x - 7} [/tex]
Cancel each pair of equal factors in the numerator and denominator.
[tex] = \dfrac{9(x + 3)}{1} [/tex]
Simplify.
[tex] = 9(x + 3) [/tex]
