Question

4/2n+5/3c=1 Solve for c. -Multiply both sides by (blank) to clear fractions.

Answer 1

Answer:

We conclude that:

$c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2$

Step-by-step explanation:

Given the expression

$\frac{4}{2n}+\frac{5}{3c}=1$

Let us solve for 'c'

$\frac{4}{2n}+\frac{5}{3c}=1$

Least Common Multiplier of 2n, 3c:   6nc

Now multiply both sides by LCM = 6nc

$\frac{4}{2n}\cdot \:6nc+\frac{5}{3c}\cdot \:6nc=1\cdot \:6nc$

Simplify

$12c+10n=6nc$

Subtract 10n from both sides

$12c+10n-10n=6nc-10n$

Simplify

$12c=6nc-10n$

Subtract 6nc from both sides

$12c-6nc=6nc-10n-6nc$

Simplify

$12c-6nc=-10n$

Factor 12c - 6nc = 6c(2-n)

$6c\left(2-n\right)=-10n$

Divide both sides by 6(2-n);  n≠2

$\frac{6c\left(2-n\right)}{6\left(2-n\right)}=\frac{-10n}{6\left(2-n\right)};\quad \:n\ne \:2$

simplify

$c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2$

Therefore, we conclude that:

$c=-\frac{5n}{3\left(-n+2\right)};\quad \:n\ne \:2$