Page:Calculus Made Easy.pdf/150

 Application to differentiation. Let it be required to differentiate $$y=\dfrac{5-4x}{6x^2+7x-3}$$; we have

If we split the given expression into

we get, however,

which is really the same result as above split into partial fractions. But the splitting, if done after differentiating, is more complicated, as will easily be seen. When we shall deal with the integration of such expressions, we shall find the splitting into partial fractions a precious auxiliary (see p. 230).

Exercises XI. (See p. 259 for Answers.)

Split into fractions:

(1) $$\dfrac{3x + 5}{(x - 3)(x + 4)}$$.

(2) $$\dfrac{3x-4}{(x-1)(x-2)}$$.

(3) $$\dfrac{3x+5}{x^2+x-12}$$.

(4) $$\dfrac{x+1}{x^2-7x+12}$$.

(5) $$\dfrac{x-8}{(2x+3)(3x-2)}$$.

(6) $$\dfrac{x^2-13x+26}{(x-2)(x-3)(x-4)}$$.