Answer
The required solution is True
Work Step by Step
We have the given algebraic expression:
$\frac{2x-1}{x-7}+\frac{3x-1}{x-7}-\frac{5x-2}{x-7}=0$
We know that for an algebraic expression, a rational expression is an expression which can be expressed in the form $\frac{p}{q}$, where, both $p\ \text{and }q$ are polynomials and the denominator $q\ne 0$.
Now, solve the left-hand side of the given algebraic expression.
$\frac{2x-1}{x-7}+\frac{3x-1}{x-7}-\frac{5x-2}{x-7}$
Because the denominator of all the fractions is the same, therefore, simply add or subtract the numerators:
$\begin{align}
& \frac{2x-1}{x-7}+\frac{3x-1}{x-7}-\frac{5x-2}{x-7}=\frac{2x-1+3x-1-\left( 5x-2 \right)}{\left( x-7 \right)} \\
& =\frac{2x-1+3x-1-5x+2}{\left( x-7 \right)} \\
& =\frac{\left( 2x+3x-5x \right)+\left( -1-1+2 \right)}{\left( x-7 \right)} \\
& =\frac{\left( 5x-5x \right)+\left( -2+2 \right)}{\left( x-7 \right)}
\end{align}$
And simplify further:
$\begin{align}
& \frac{2x-1}{x-7}+\frac{3x-1}{x-7}-\frac{5x-2}{x-7}=\frac{\left( 5x-5x \right)+\left( -2+2 \right)}{\left( x-7 \right)} \\
& =\frac{0}{\left( x-7 \right)} \\
& =0
\end{align}$
Thus, $\frac{2x-1}{x-7}+\frac{3x-1}{x-7}-\frac{5x-2}{x-7}=0$. Hence, the given statement is True.
