Simplify the expression completely:

4x^2+2x-42/4x /(x-3)

(x (8 x^2 - 20 x + -33))/(2 (x - 3))

Step-by-step explanation:

Simplify the following:

4 x^2 + 2 x - (42 x)/(4 (x - 3))

The gcd of 42 and 4 is 2, so 42/4 = (2×21)/(2×2) = 2/2×21/2 = 21/2:

4 x^2 + 2 x - x/(x - 3) 21/2

Put each term in 4 x^2 + 2 x - (21 x)/(2 (x - 3)) over the common denominator 2 (x - 3): 4 x^2 + 2 x - (21 x)/(2 (x - 3)) = (8 (x - 3) x^2)/(2 (x - 3)) + (4 (x - 3) x)/(2 (x - 3)) - (21 x)/(2 (x - 3)):

(8 x^2 (x - 3))/(2 (x - 3)) + (4 x (x - 3))/(2 (x - 3)) - (21 x)/(2 (x - 3))

(8 (x - 3) x^2)/(2 (x - 3)) + (4 (x - 3) x)/(2 (x - 3)) - (21 x)/(2 (x - 3)) = (8 (x - 3) x^2 + 4 (x - 3) x - 21 x)/(2 (x - 3)):

(8 x^2 (x - 3) + 4 x (x - 3) - 21 x)/(2 (x - 3))

Factor x out of 8 (x - 3) x^2 + 4 (x - 3) x - 21 x, resulting in x (8 (x - 3) x^(2 - 1) + 4 (x - 3) - 21):

(x (8 x^(2 - 1) (x - 3) + 4 (x - 3) - 21))/(2 (x - 3))

2 - 1 = 1:

(x (8 x (x - 3) + 4 (x - 3) - 21))/(2 (x - 3))

8 x (x - 3) = 8 x^2 - 24 x:

(x (8 x^2 - 24 x + 4 (x - 3) - 21))/(2 (x - 3))

4 (x - 3) = 4 x - 12:

(x (4 x - 12 + 8 x^2 - 24 x - 21))/(2 (x - 3))

Grouping like terms, 8 x^2 + 4 x - 24 x - 21 - 12 = 8 x^2 + (-24 x + 4 x) + (-12 - 21):

(x (8 x^2 + (-24 x + 4 x) + (-12 - 21)))/(2 (x - 3))

4 x - 24 x = -20 x:

(x (8 x^2 + -20 x + (-12 - 21)))/(2 (x - 3))

-12 - 21 = -33:

(x (8 x^2 - 20 x + -33))/(2 (x - 3))

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.