Simplify Sx 9 Solution33 x5x9 x2 39 x25x3 x 332 x25x3 x 3

Solution

[3/(3 -x)]/[5x/(9 -x²)]

= 3(9 -x²)/[5x(3 -x)]

= 3(3² -x²)/[5x(3 -x)]

= 3(3 -x)(3 +x)/[5x(3 -x)]           since a² -b² = (a +b)(a -b)

= 3(3 +x)/(5x)

= (9 + 3x)/(5x)

= 9/(5x) + (3x)/(5x)

= 9/(5x) + (3/5)

Hence [3/(3 -x)]/[5x/(9 -x²)] = 9/(5x) + (3/5)