the simplified form is
![\frac{x^2(2x+3)}{2(4x-3)}](/tex.php?f=\frac{x^2(2x+3)}{2(4x-3)})
step-by-step explanation:
we want to simplify the expression,
![\frac{\frac{6x+9}{15x^2} }{\frac{16x-12}{10x^4} }](/tex.php?f=\frac{\frac{6x+9}{15x^2} }{\frac{16x-12}{10x^4} })
let us change the middle bar to a normal division sign to obtain,
![\frac{6x+9}{15x^2}\div\frac{16x-12}{10x^4}](/tex.php?f=\frac{6x+9}{15x^2}\div\frac{16x-12}{10x^4})
we multiply the first fraction by the reciprocal of the second fraction to obtain,
![\frac{6x+9}{15x^2}\times \frac{10x^4}{16x-12}](/tex.php?f=\frac{6x+9}{15x^2}\times \frac{10x^4}{16x-12})
we factor to obtain,
![\frac{3(2x+3)}{3\times5\times x^2}\times \frac{2\times5\times x^2\times x^2}{4(4x-3)}](/tex.php?f=\frac{3(2x+3)}{3\times5\times x^2}\times \frac{2\times5\times x^2\times x^2}{4(4x-3)})
we cancel the common factors to get,
![\frac{(2x+3)}{1}\times \frac{ x^2}{2(4x-3)}](/tex.php?f=\frac{(2x+3)}{1}\times \frac{ x^2}{2(4x-3)})
we simplify to get,
![\frac{x^2(2x+3)}{2(4x-3)}](/tex.php?f=\frac{x^2(2x+3)}{2(4x-3)})
the correct answer is b