To simplify the given expression [tex]\(\frac{7x^2 + 5x}{x}\)[/tex], follow these steps:
1. Expression Analysis: The numerator of the expression is [tex]\(7x^2 + 5x\)[/tex], and the denominator is [tex]\(x\)[/tex].
2. Factor the Numerator: Notice that the numerator [tex]\(7x^2 + 5x\)[/tex] can be factored by taking [tex]\(x\)[/tex] as a common factor:
[tex]\[
7x^2 + 5x = x(7x + 5)
\][/tex]
3. Rewrite the Expression: Substitute the factored form back into the original expression:
[tex]\[
\frac{7x^2 + 5x}{x} = \frac{x(7x + 5)}{x}
\][/tex]
4. Simplify the Fraction: Since [tex]\(x \neq 0\)[/tex], we can cancel out the [tex]\(x\)[/tex] in the numerator and the denominator:
[tex]\[
\frac{x(7x + 5)}{x} = 7x + 5
\][/tex]
Hence, the simplified form of the given expression is:
[tex]\[
7x + 5
\][/tex]
