How do you simplify and find the restrictions for #3/(x-4)-7#?

Question

Ethan Adkins · Accepted Answer

Restriction: #color(red)(x!=4)#
Simplification (maybe): #color(blue)((31-7x)/(x-4))# Since division by #0# is undefined. #x-4!=0color(white)("xxx")rarrcolor(white)("xxx")x!=4# What is considered a "simplification" is more problematic. Here is one possibility: #color(white)("XXX")3/(x-4)-7# #color(white)("XXXXXX")=3/(x-4)-(7(x-4))/(x-4)# #color(white)("XXXXXX")=3/(x-4)-(7x-28)/4# #color(white)("XXXXXX")=(3-7x+28)/(x-4)# #color(white)("XXXXXX")=(31-7x)/(x-4)#

Savannah Anderson · Answer

undefined To simplify the expression 3/(x-4)-7, we can combine the terms by finding a common denominator. The common denominator is (x-4).

Multiplying the first term by (x-4)/(x-4), we get 3(x-4)/(x-4) - 7(x-4)/(x-4).

Simplifying further, we have (3x-12)/(x-4) - (7x-28)/(x-4).

Combining the terms, we get (3x-12-7x+28)/(x-4).

Simplifying the numerator, we have (-4x+16)/(x-4).

The restrictions for this expression occur when the denominator is equal to zero. Therefore, x-4 cannot be equal to zero.

Solving x-4=0, we find that x cannot be equal to 4.

Hence, the simplified expression is (-4x+16)/(x-4) and the restriction is x ≠ 4.