Question

Solve the following question

Answer 1

g)
`u^(4)\cdot v^(-1)\cdot z^(3)`, h)
`((x+4)\cdot (x+2))/(3\cdot (x-5))`

Explanation:

We proceed to solve each equation by algebraic means:

g)
`(u^(5)\cdot v)/(z)/ (u\cdot v^(2))/(z^(4))`

1)
`(u^(5)\cdot v)/(z)/ (u\cdot v^(2))/(z^(4))` Given

2)
`((u^(5)\cdot v)/(z) )/((u\cdot v^(2))/(z^(4)) )` Definition of division

3)
`(u^(5)\cdot v\cdot z^(4))/(u\cdot v^(2)\cdot z)`
`((a)/(b) )/((c)/(d) ) = (a\cdot d)/(b\cdot c)`

4)
`\left((u^(5))/(u) \right)\cdot \left((v)/(v^(2)) \right)\cdot \left((z^(4))/(z) \right)` Associative property

5)
`u^(4)\cdot v^(-1)\cdot z^(3)`
`(a^(m))/(a^(n)) = a^(m-n)`/Result

h)
`(x^(2)-16)/(x^(2)-10\cdot x + 25) / (3\cdot x - 12)/(x^(2)-3\cdot x -10)`

1)
`(x^(2)-16)/(x^(2)-10\cdot x + 25) / (3\cdot x - 12)/(x^(2)-3\cdot x -10)` Given

2)
`((x^(2)-16)/(x^(2)-10\cdot x+25) )/((3\cdot x - 12)/(x^(2)-3\cdot x - 10) )` Definition of division

3)
`((x^(2)-16)\cdot (x^(2)-3\cdot x -10))/((x^(2)-10\cdot x + 25)\cdot (3\cdot x - 12))`
`((a)/(b) )/((c)/(d) ) = (a\cdot d)/(b\cdot c)`

4)
`((x+4)\cdot (x-4)\cdot (x-5)\cdot (x+2))/(3\cdot (x-5)^(2)\cdot (x-4) )` Factorization/Distributive property

5)
`\left((1)/(3) \right)\cdot (x+4)\cdot (x+2)\cdot \left((x-4)/(x-4) \right)\cdot \left[(x-5)/((x-5)^(2)) \right]` Modulative and commutative properties/Associative property

6)
`((x+4)\cdot (x+2))/(3\cdot (x-5))`
`(a^(m))/(a^(n)) = a^(m-n)`/
`(a)/(b)* (c)/(d) = (a\cdot c)/(b\cdot d)`/Definition of division/Result