To find the value of the expression [tex]\(\frac{4x - y}{2y + x}\)[/tex] when [tex]\(x = 3\)[/tex] and [tex]\(y = 3\)[/tex], follow these detailed steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
\frac{4 \cdot 3 - 3}{2 \cdot 3 + 3}
\][/tex]
2. Calculate the numerator:
[tex]\[
4 \cdot 3 - 3 = 12 - 3 = 9
\][/tex]
3. Calculate the denominator:
[tex]\[
2 \cdot 3 + 3 = 6 + 3 = 9
\][/tex]
4. Form the new fraction with the calculated numerator and denominator:
[tex]\[
\frac{9}{9}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{9}{9} = 1
\][/tex]
Thus, the value of the expression when [tex]\(x = 3\)[/tex] and [tex]\(y = 3\)[/tex] is [tex]\(\boxed{1}\)[/tex].
