Solve: x/x-1 = x/2 - (x+1)/(x+2) Simplify: x^2+x-20/ (5x-20) Multiply: (x^2-x-6)/(x^2+4x+3) *(times) (x^2-x-12)/(x^2-2x-8)Please show step- by-...

Solve:

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

Go by pririty rules operations PEDMAS. RHS convert the fractions under the common denominator:

1-1={x(x+2)-2(x+1)}/(x+2)

Mutiply by the denominator, (x+2) both sides:

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

0=x^2+2x-2x-2

0=x^2-2

x^2=2

x=sqrt(2)  or  x=-sqrt(2)

Simplification:

To simplify :x^2+x-20/(5x-20)= x^2+x-20/({5(x-4)}

=x^2+x-4/(x-4). There is no further simplification.

But if you intend x^2+x-20 is to be divided by (5x-20),Then it requires that you should write it like: (x^2+x-20)/(5x-20)

Then, x^2+x-20=(x+5)(x-4) is dividendo

(5x-20)= 5(x-4) is divisor. Therefore x^2+x-20 divided by 5x-20

is (x^2+x-20)(5x-20)= (x+5)(x-4)/{5(x-4)}=(x+5)/5 or x/5+1

Multiplication:

(x^2-x-6)/(x^2+4x+3)*(x^2-x-12)/(x^2-2x+3)

(x-3)(x+2)/[(x+3)(x+1)] * (x-4)(x+3)/[(x-3)(x+1)]

(x-3)(x+2)(x-4)(x+3)/ [(x+3)(x+1)(x-3)(x+1)]

=(x+2){x-4)/(x+1)^2=(x^2-2x-8)/(x^2+2x+1)