Question
Question: Solve the expression; \(\dfrac{x+3}{x-2}-\dfrac{1-x}{x}=\dfrac{17}{x}\left( x\ne 0,2 \right)\)...
Solve the expression;
x−2x+3−x1−x=x17(x=0,2)
Solution
We solve this question by bringing the term in RHS to LHS. Then we simplify the terms with the same denominator. Then we take the LCM of the denominators of the two fractions and multiply each fraction with corresponding variables to get the denominator of both fractions as LCM. Then we add the numerators and then simplify them to get an equation. Then we find the roots of the equation using the formula for the roots of the quadratic equation ax2+bx+c=0, x=2a−b±b2−4ac. Then we simplify the obtained values to find the values of x.
Complete step-by-step solution
We are given that x−2x+3−x1−x=x17.
We are also given that x=0,2.
So, now let us consider the given equation.
⇒x−2x+3−x1−x=x17
Now let us bring the expression x17 to the LHS. Then the equation becomes,