Question

solve for x;
$\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = \frac{10}{3}$
where (x is not equal to 2,4)​

Answer 1

Answer:

Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,

\[\frac{x^{2} + 3x}{x + 3}\]

has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.

\begin{align*} \frac{{x}^{2} + 3x}{x + 3} & = \frac{x\left(x + 3\right)}{x + 3}\\ & =x \qquad \qquad \left(x\ne -3\right) \end{align*}

If \(x=-3\) then the denominator, \(x + 3 = 0\) and the fraction is undefined.