Question

Simplify. From Algebra. Plz help me​

Answer 1

Answer:

$\frac{a}{(a-c)\cdot (b-c)}$

Step-by-step explanation:

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

1) $\frac{a}{(a-b)\cdot (a-c)} + \frac{b}{(b-c)\dot (b-a) } + \frac{c}{(a-c)\cdot (b-c)}$ Given.

2) $\frac{a}{(a-b)\cdot (a-c)} + \frac{b}{-(a-b)\cdot (b-c)} + \frac{c}{(a-c)\cdot (b-c)}$ Commutative property/Distributive property/$(-1)\cdot a = -a$/$(-1)\cdot (-a) = a$

3) $\frac{a}{(a-b)\cdot (a-c)} + \frac{(-b)}{(a-b)\cdot (b-c)} + \frac{c}{(a-c)\cdot (b-c)}$    $-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}$

4) $\frac{a\cdot (b-c)}{(a- b)\cdot (a-c)\cdot (b-c)} + \frac{(-b)\cdot (a-c)}{(a-b)\cdot (b-c)\cdot (a-c)} + \frac{c\cdot (a-b)}{(a-c)\cdot (b-c)\cdot (a-b)}$ Modulative property/Existence of aditive inverse/Definition of division

5) $\frac{a\cdot (a-c) + (-b)\cdot (a-c)+c\cdot (a-b)}{(a-b)\cdot (a-c)\cdot (b-c)}$ Distributive property/Definition of division

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

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

8) $\frac{a\cdot (a-b)}{(a-b)\cdot (a-c)\cdot (b-c)}$ Commutative property

9) $\frac{a}{(a-c)\cdot (b-c)}$ Commutative and associative properties/Existence of multiplicative inverse/Result