Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac { \frac { a ^ { 2 } } { x - a } + \frac { b ^ { 2 } } { x - b } + \frac { c ^ { 2 } } { x - c } + a + b + c } { \frac { a } { x - a } + \frac { b } { x - b } + \frac { c } { x - c } }$$

Answer

$$2*h*(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)*((x-a)*(x-b)*(x-c))/(a*(x-b)*(x-c)+b*(x-a)*(x-c)+c*(x-a)*(x-b))$$

Solution


Rewrite the expression with a common denominator.
\[\frac{\frac{{a}^{2}}{x-a}+\frac{{b}^{2}}{x-b}+\frac{{c}^{2}}{x-c}+a+b+c}{\frac{a(x-b)(x-c)+b(x-a)(x-c)+c(x-a)(x-b)}{(x-a)(x-b)(x-c)}}h\times 2\]
Invert and multiply.
\[(\frac{{a}^{2}}{x-a}+\frac{{b}^{2}}{x-b}+\frac{{c}^{2}}{x-c}+a+b+c)\times \frac{(x-a)(x-b)(x-c)}{a(x-b)(x-c)+b(x-a)(x-c)+c(x-a)(x-b)}h\times 2\]
Regroup terms.
\[2h(\frac{{a}^{2}}{x-a}+\frac{{b}^{2}}{x-b}+\frac{{c}^{2}}{x-c}+a+b+c)\times \frac{(x-a)(x-b)(x-c)}{a(x-b)(x-c)+b(x-a)(x-c)+c(x-a)(x-b)}\]
[email protected]
Privacy Policy | Terms & Conditions
Contact Us