F4 Math - Polynomiais etc

1.1/(x^2－1)+1/(x－1)=0
Sol
1/(x^2－1)+1/(x－1)=0
1+(x+1)=0
x=－2

2. x-y=0，x^2－xy+y^2=5
Sol
x=y
x^2－x^2+x^2=5
x^2=5
x=+/-√5(1)x=√5，y=√5
(2)x=－√5，y=－√5

3. x+y=1，x^2－xy=15
Sol
y=1－x
x^2－x(1－x)=15
x^2－x+x^2=15
2x^2－x－15=0
(2x+5)(x－3)=0
x=－5/2 or x=3
(1) x=－5/2，y=7/2
(2) x=3，y=-2


4.[(6x^2－7x－20)/(x^2－4)]*[(x^2－x－2)/(6x－15)]/[(3x^2+7x+4)/(x^2+2x)]
Sol
[(6x^2－7x－20)/(x^2－4)]*[(x^2－x－2)/(6x－15)]/[(3x^2+7x+4)/(x+2+2x)]
=[(6x^2－7x－20)/(x^2－4)]*[(x^2－x－2)/(6x－15)]*[(x^2+2x)/(3x^2+7x+4)]
=[(6x^2－7x－20)*(x^2－x－2)*(x^2+2x)]/[(x^2－4)*(6x－15)*(3x^2+7x+4)]
=[(2x－5)(3x+4)*(x－2)(x+1)*x(x+2)]/[(x－2)(x+2)*3*(2x－5)*(x+1)(3x+4)]
=x/3

5. a/[(a－b)(a－c)+b/[(b－c)(b－a)]+c/](c－a)(c－b)]
Sol
A=a/[(a－b)(a－c)+b/[(b－c)(b－a)]+c/](c－a)(c－b)]
A(a－b)(b－c)(c－a)
=a(c－b)+b(a－c)+c(b－a)
=ac－ab+ab－bc+bc－ac
=0