Questions: Simplify. 35 x^2(x+7)(2 x-5)/30 x^4(x+7)^5

Solution Steps

First, identify and factor out any common terms in the numerator and the denominator. The expression is:

\[ \frac{35 x^{2}(x+7)(2 x-5)}{30 x^{4}(x+7)^{5}} \]

Notice that both the numerator and the denominator have common factors of \(x^2\) and \((x+7)\).

• Cancel \(x^2\) from both the numerator and the denominator:

\[ \frac{35 (x+7)(2 x-5)}{30 x^{2}(x+7)^{5}} \]

• Cancel one \((x+7)\) from both the numerator and the denominator:

\[ \frac{35 (2 x-5)}{30 x^{2}(x+7)^{4}} \]

Now, simplify the coefficients \(\frac{35}{30}\):

• The greatest common divisor of 35 and 30 is 5. Divide both by 5:

\[ \frac{7 (2 x-5)}{6 x^{2}(x+7)^{4}} \]

Final Answer