Question

Rewrite as equivalent rational expressions with denominator (3m−4)(m+8)(m−7):

63m2+20m−32,3m3m2−25m+28

Answer 1

To rewrite the given rational expressions with the given denominator, we need to cancel out common factors in the numerator and denominator.

Step-by-step explanation:

To rewrite the given rational expressions with denominator (3m−4)(m+8)(m−7), we need to cancel out any common factors in the numerator and denominator.

• For the expression 63m^2 + 20m − 32, we can factor out a common factor of (m−4). So, the equivalent rational expression is: (m−4)(63m + 8).
• For the expression 3m^2 − 25m + 28, we cannot factor out any common factors. So, the equivalent rational expression is: 3m^2 − 25m + 28.

Answer 2

The first rational expression is 63m²+20m−32. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), first we need to find the LCD (Lowest Common Denominator) of both terms. So, we need to multiply each numerator and denominator of the first rational expression by (3m−4)(m+8)(m−7).

In the numerator, we need to multiply 63m² by (3m−4)(m+8)(m−7):

63m² × (3m−4)(m+8)(m−7) = 63m³ - 224m² + 784m - 504

In the denominator, we need to multiply 1 by (3m−4)(m+8)(m−7):

1 × (3m−4)(m+8)(m−7) = 3m³ - 12m² + 24m - 16

Therefore, the rewritten rational expression is:

63m³ - 224m² + 784m - 504/3m³ - 12m² + 24m - 16

The second rational expression is 3m³m²−25m+28. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), we first need to find