Which expression is equivalent to the expression below?(6c^2+3c/-4c+2)/(2c+1/4c-2)

We need to simplify this expression. The rational expression in the denominator can be multiplied to numerator by taking its reciprocal as shown below:

[tex]\frac{\frac{6c^{2}+3c}{-4c+2}}{\frac{2c+1}{4c-2}} \\\\ =\frac{6c^{2}+3c}{-4c+2} \times \frac{4c-2}{2c+1}\\\\=\frac{3c(2c+1)}{-(4c-2)} \times \frac{4c-2}{2c+1}\\\\ =-3c[/tex]

Thus, the given expression in simplified form is equal to -3c

lublana lublana · Answer 2 · 2019-08-13T13:07:55+02:00

Answer:

-3c

Step-by-step explanation:

We are given that an expression

[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]

We have to find an expression which is equal to given expression

Taking common 3c from nominator and -2 from denominator in dividened and 2 common in divisor then we get

[tex]\frac{\frac{3c(2c+1)}{-2(c-2)}}{\frac{2c+1}{2(2c-1)}}[/tex]

[tex]\frac{3c(2c+1)}{-2(2c-1)}\times \frac{2(2c-1)}{(2c+1)}[/tex]

By reciprocal divisor

By canceling same factor

Then ,we get

[tex]\frac{\frac{6c^2+3c}{-4c+2}}{\frac{2c+1}{4c-2}}[/tex]

=-3c