Questions: Multiply and simplify: [ (x^2-25)/(x^2+2 x-35) cdot (x+7)/(3 x) ]

Solution Steps

To multiply and simplify the given expression, first factor the polynomials in the numerator and the denominator. Then, multiply the fractions by multiplying the numerators together and the denominators together. Finally, simplify the resulting expression by canceling out any common factors.

We start by factoring the expressions in the numerator and denominator:

• The numerator \( x^2 - 25 \) factors to \( (x - 5)(x + 5) \).
• The denominator \( x^2 + 2x - 35 \) factors to \( (x - 5)(x + 7) \).

Next, we multiply the fractions:

\[ \frac{(x - 5)(x + 5)}{(x - 5)(x + 7)} \cdot \frac{x + 7}{3x} \]

This results in:

\[ \frac{(x - 5)(x + 5)(x + 7)}{3x(x - 5)(x + 7)} \]

Now, we simplify the expression by canceling out the common factors \( (x - 5) \) and \( (x + 7) \):

\[ \frac{(x + 5)}{3x} \]

Final Answer