Question

(x^2-x)y^2+y-(x^2+x)​

Answer 1

Answer:

Can someone factorise (x^2-x) y^2+y-(x^2+x)?

Given equation is,

(x^2-x) y^2+y-(x^2+x)

It is Quadratic equation in y of form

a*y^2+b*y+c

Here,

a= x(x-1) , b= 1 , c= x(x+1);

where a!=0

Solutions to this equation are,

y= [-b+(b^2 - 4ac)]/2a , y= [-b-(b^2 - 4ac)]/2a ;

Thus, Substituting values,

b^2–4ac= 1- (4x^2)*(x^2–1)

-b+ b^2–4ac = (4x^2)(x^2–1)

y= (4x^2)(x^2–1)/x(x-1)

y= 4x(x+1)

Now,

Product of roots is c/a

c/a= x(x+1)/x(x-1) = (x+1)/(x-1) ;

Thus,

y*4x(x-1) = (x+1)/(x-1) ;

y= (x+1)/ [4x(x-1)]

Thus, factors of this equation are,

y= 4x(x+1) and y= (x+1)/ [4x(x-1)]

List of Formulas:

1. a^2 - b^2 = (a+b)(a-b)

2. ab-ac = a(b-c)

Answer 2

Step-by-step explanation:

(x(x^2-x)y^2+y-(x^2+x)-x