[tex]\dfrac1{c-3}-\dfrac1c=\dfrac3{c(c-3)}[/tex]
Combining the fractions on the left gives us
[tex]\dfrac c{c(c-3)}-\dfrac{c-3}{c(c-3)}=\dfrac{c-(c-3)}{c(c-3)}=\dfrac3{c(c-3)}[/tex]
which is defined only as long as [tex]c\neq0[/tex] and [tex]c\neq3[/tex].
This expression is the same as the one on the right:
[tex]\dfrac3{c(c-3)}=\dfrac3{c(c-3)}[/tex]
so and value of [tex]c[/tex], except [tex]c=0[/tex] and [tex]c=3[/tex] for the reason mentioned earlier, will be a solution, so the answer is C.
The solution of the expression is all real numbers except c = 3 and c = 0 the option (C) all real numbers, except c ≠ 0 and c ≠ 3 is correct.
It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm \dfrac{1}{c-3}-\dfrac{1}{c}=\dfrac{3}{c(c-3)}[/tex]
After simplify:
[tex]\rm \dfrac{3}{c(c-3)}=\dfrac{3}{c(c-3)}[/tex]
If we plug c = 3 and c = 0 the expression will not give a real value, it will be undefined.
Thus, the solution of the expression is all real numbers except c = 3 and c = 0 the option (C) all real numbers, except c ≠ 0 and c ≠ 3 is correct.
Learn more about the expression here:
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