Question

solve by factorisation

1]  1/a+b+x=1/a+1/b+1/x                     [a+bis not 0]
2]   a[x^2+1]-x[a^2+1}=0
3]    x^2-x-a[a+1]=0

plz with aall steps

Answer 1

2. ax(x-a)-(x-a)=0 ⇒ (x-a)(ax-1)=0 hence, x=a or 1/a. 3. (x²-a²)-(x+a)=0 ⇒ (x-a-1)(x+a)=0 hence, x=-a or a+1. The first one is a big one. (a+b+x)(ab+{a+b}x)=abx. .......... you get this after simplifying R.H.S. and taking reciprocals on both sides. Hence after this you get, x²(a+b)+x(a+b)²+ab(a+b)+abx=abx. Then x²+(a+b)x+ab=0. ⇒ (x+a)(x+b)=0 Hence, x=-a or-b