How do you solve $\frac{2}{3} = 2 - \frac{5 x - 3}{x - 1}$ $2/3 = 2 - (5x-3)/(x-1)$ ?

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Answer 1 · 2018-06-25T21:29:52

$x = \frac{5}{11}$ $x=5/11$

Let's subtract $2$ $2$ from both sides to get

$\frac{2}{3} - \frac{6}{3} = - \frac{5 x - 3}{x - 1}$ $2/3-6/3=-(5x-3)/(x-1)$

$\Rightarrow - \frac{4}{3} = - \frac{5 x - 3}{x - 1}$ $=>-4/3=-(5x-3)/(x-1)$

To get rid of the $x - 1$ $x-1$ in the denominator, let's multiply both sides by it. This gives us

$\frac{- 4 (x - 1)}{3} = - (5 x - 3)$ $(-4(x-1))/3=-(5x-3)$

We can also get rid of the $3$ $3$ in the denominator by multiplying both sides by it. We get

$- 4 (x - 1) = - 3 (5 x - 3)$ $-4(x-1)=-3(5x-3)$

Let's distribute the $- 4$ $-4$ and $- 3$ $-3$ to their respective terms to get

$- 4 x + 4 = - 15 x + 9$ $-4x+4=-15x+9$

Adding $15 x$ $15x$ on both sides gives us

$11 x + 4 = 9$ $11x+4=9$

Subtracting $4$ $4$ from both sides, we get

$11 x = 5$ $11x=5$

Lastly, dividing both sides by $11$ $11$ gives us

$x = \frac{5}{11}$ $x=5/11$

Hope this helps!

How do you solve 2/3 = 2 - (5x-3)/(x-1)23=2−5x−3x−1 2/3 = 2 - (5x-3)/(x-1)?