Write the function as a sum of partial fractions. Do not determine the numerical values of the coefficients.(a) x/x^2+xâ2(b) 6âx/x^2â3xâ54

The correct equations in the question are:

(a)   (b)

Step-by-step explanation:

From above:

a)  

We are to find the roots of the quadratic equation at the denominator.

i.e.

x²+x-2 =  x² + 2x - x - 2

= x(x+2) - 1(x+2)

= (x -1 ) (x + 2)

Thus;

b)

The quadratic equation roots can be calculated by finding two numbers that if we multiply then, we will get -54 and if we add or subtract them, we will get -3

x²-3x -54 =  x² - 9x +6x - 54

=  x(x-9) + 6(x-9)

= (x + 6) (x - 9)

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step-by-step explanation:

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step-by-step explanation: