Question 29

If $$a+b=2c$$, then the value of $$\frac{a}{a-c}+\frac{b}{b-c}$$ is

Solution

Since, $$a+b=2c$$

or, $$b-c=c-a$$

So, $$\dfrac{a}{a-c}+\dfrac{b}{b-c}$$

=$$\dfrac{a}{a-c}+\dfrac{b}{c-a}$$

=$$\dfrac{a}{a-c}-\dfrac{b}{a-c}$$

=$$\dfrac{a-b}{a-c}$$

Substituting $$a+b=2c$$,

=$$\dfrac{a-b}{a-\dfrac{\left(a+b\right)}{2}}$$

=$$\dfrac{a-b}{\dfrac{2a-a-b}{2}}$$

=$$\dfrac{a-b}{\dfrac{a-b}{2}}$$

=$$\dfrac{2\left(a-b\right)}{\left(a-b\right)}$$

=$$2$$

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