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Mathematics Question on Limits and derivations

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): px2+qx+rax+b\frac{px^2+qx+r}{ax+b}

Answer

=−apx−2bpx+ar−bq(px2+qx+r)2\frac{-apx-2bpx+ar-bq}{(px^2+qx+r)^2}
Let f (x)= px2+qx+rax+b\frac{px^2+qx+r}{ax+b}
By quotient rule,
f'(x)= (ax+b)ddx\frac{d}{dx}(px2+qx+r)- (px2 +qx+r)\frac{d}{dx}$$\frac{(ax+b)}{(ax+b)^2}
=(ax+b)(2px + q) -(px2+qx+r)(a)(ax+b)2\frac{(a)}{(ax+b)^2}
=−apx2+2bpx+bq−ar(ax+b)2\frac{-apx^2+2bpx+bq-ar}{(ax+b)^2}