Question

G/(g ^ 2 + 4g) - g/((g + 4) ^ 2) =?
Simplify.

Answer 1

`(4)/((g + 4) ^(2) )`

Explanation:

• Factor the expressions that are not already factored in g/g² + 4g.

`(g)/(g(g + 4)) - (g)/((g + 4) ^(2) )`

• Cancel out g in both numerator and denominator.

`(1)/(g + 4) - (g)/((g + 4) ^(2) )`

• To add or subtract expressions, expand them to make their denominators the same. Least common multiple of g+4 and (g+4)² is (g+4)². Multiply 1/g + 4 times g + 4/g + 4.

`(g + 4)/((g + 4) ^(2) ) - (g)/((g + 4) ^(2) )`

• Since g + 4/(g + 4)² and g/( g + 4)⁴ have the same denominator, subtract them by subtracting their numerators.

`(g + 4 - g)/((g + 4) ^(2) )`

• Combine like terms in g+4−g.

`(4)/((g + 4) ^(2) )`

• Expand (g + 4)².

`(4)/(g^(2) + 8g + 16 )`

Hope It's Help