Simplify. (7v-21)/(v-3)*(v+10)/(7v-42)

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Factor Common Factors: Factor out the common factors in the numerators and denominators. The expression given is (7v-21)/(v-3)*(v+10)/(7v-42). We can factor out a 7 from the terms 7v-21 and 7v-42, and we can factor out a 3 from the term v-3.Factoring Numerators and Denominators: Factoring the numerators and denominators. The factored form of 7v-21 is 7(v-3) because 7 * (v-3) = 7v-21. The factored form of 7v-42 is 7(v-6) because 7 * (v-6) = 7v-42. The denominator v-3 is already factored. Now we rewrite the expression with the factored terms: (7(v-3))/(v-3)*(v+10)/(7(v-6))Cancel Common Factors: Cancel out the common factors. We can cancel the (v-3) term in the numerator of the first fraction with the (v-3) in the denominator because they are the same and not equal to zero (since v cannot be 3, otherwise the denominator would be zero which is not allowed). Now we have: 7*(v+10)/(7(v-6))Cancel Factor of 7: Cancel out the common factor of 7. We can cancel the 7 in the numerator with the 7 in the denominator. Now the expression simplifies to: (v+10)/(v-6)Check Further Simplifications: Check for any further simplifications. The expression (v+10)/(v-6) cannot be simplified further because there are no common factors left to cancel out.

Simplify. $\frac{7 v-21}{v-3} \cdot \frac{v+10}{7 v-42}$

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Simplify. $\frac{7 v-21}{v-3} \cdot \frac{v+10}{7 v-42}$