How do you combine #[(3x + 2y)/(x - y^2)] - [(2x - 3y)/(x^2 - y)] + [(5x + y)/(y - x^2)]#?

Question

Kennedy Adams · Accepted Answer

Have a look, but check my maths!

Jameson Allen · Answer

undefined To combine the given expression, we need to find a common denominator for all the fractions involved. The common denominator is (x - y^2)(x^2 - y)(y - x^2).

Next, we multiply each fraction by the appropriate factors to obtain the common denominator.

For the first fraction, we multiply the numerator and denominator by (x^2 - y)(y - x^2). 
[(3x + 2y)/(x - y^2)] * [(x^2 - y)(y - x^2)/(x^2 - y)(y - x^2)] = (3x + 2y)(x^2 - y)(y - x^2)/(x - y^2)(x^2 - y)(y - x^2)

For the second fraction, we multiply the numerator and denominator by (x - y^2)(y - x^2). 
[(2x - 3y)/(x^2 - y)] * [(x - y^2)(y - x^2)/(x - y^2)(y - x^2)] = (2x - 3y)(x - y^2)(y - x^2)/(x^2 - y)(x - y^2)(y - x^2)

For the third fraction, we multiply the numerator and denominator by (x - y^2)(x^2 - y). 
[(5x + y)/(y - x^2)] * [(x - y^2)(x^2 - y)/(x - y^2)(x^2 - y)] = (5x + y)(x - y^2)(x^2 - y)/(y - x^2)(x - y^2)(x^2 - y)

Now, we can combine the fractions by adding the numerators and keeping the common denominator.

[(3x + 2y)(x^2 - y)(y - x^2) - (2x - 3y)(x - y^2)(y - x^2) + (5x + y)(x - y^2)(x^2 - y)] / (x - y^2)(x^2 - y)(y - x^2)