Question

Simplify. From Algebra. Plz help me​

Answer 1

`(a)/((a-c)\cdot (b-c))`

Explanation:

We must use algebraic means to simplify the equation given. The procedure is presented below:

1)
`(a)/((a-b)\cdot (a-c)) + (b)/((b-c)\dot (b-a) ) + (c)/((a-c)\cdot (b-c))` Given.

2)
`(a)/((a-b)\cdot (a-c)) + (b)/(-(a-b)\cdot (b-c)) + (c)/((a-c)\cdot (b-c))` Commutative property/Distributive property/
`(-1)\cdot a = -a`/
`(-1)\cdot (-a) = a`

3)
`(a)/((a-b)\cdot (a-c)) + ((-b))/((a-b)\cdot (b-c)) + (c)/((a-c)\cdot (b-c))`
`-(a)/(b) = (-a)/(b) = (a)/(-b)`

4)
`(a\cdot (b-c))/((a- b)\cdot (a-c)\cdot (b-c)) + ((-b)\cdot (a-c))/((a-b)\cdot (b-c)\cdot (a-c)) + (c\cdot (a-b))/((a-c)\cdot (b-c)\cdot (a-b))` Modulative property/Existence of aditive inverse/Definition of division

5)
`(a\cdot (a-c) + (-b)\cdot (a-c)+c\cdot (a-b))/((a-b)\cdot (a-c)\cdot (b-c))` Distributive property/Definition of division

6)
`(a^(2)-a\cdot c -a\cdot b + b\cdot c+a\cdot c-b\cdot c)/((a-b)\cdot (a-c)\cdot (b-c))` Distributive and commutative properties/
`(-a) \cdot b = -a\cdot b`/
`(-a)\cdot (-b) = a\cdot b`/Definition of power

7)
`(a^(2)-a\cdot b)/((a-b)\cdot (a-c)\cdot (b-c))` Commutative, associative and modulative properties/Existence of additive inverse

8)
`(a\cdot (a-b))/((a-b)\cdot (a-c)\cdot (b-c))` Commutative property

9)
`(a)/((a-c)\cdot (b-c))` Commutative and associative properties/Existence of multiplicative inverse/Result