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How do you solve #2 + (3/(x-1)) = 10#?

Answer 1

Nathan Axel

You must start by putting on an equal denominator.

The LCD (least common denominator) is #x - 1#

#(2(x - 1))/(x - 1) + 3/(x - 1) = (10(x - 1))/(x - 1)#

At this point, we can solve by removing the denominators.

#2x - 2 + 3 = 10x - 10#

#11 = 8x#

#11/8 = x#

Practice tasks:

#(2)/(2x + 3) + 3/(x - 1) = 5/(x - 1)#

Challenge issue:

Solve for x: #1/x + 1/(xy) = 2/(y + x)#

Wishing you luck!

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Answer 2

Eli Assouline

To solve the equation 2 + (3/(x-1)) = 10, you can follow these steps:

Start by subtracting 2 from both sides of the equation to isolate the fraction: (3/(x-1)) = 8.
Multiply both sides of the equation by (x-1) to eliminate the fraction: 3 = 8(x-1).
Distribute 8 to both terms inside the parentheses: 3 = 8x - 8.
Add 8 to both sides of the equation to isolate the variable term: 11 = 8x.
Finally, divide both sides of the equation by 8 to solve for x: x = 11/8.

Therefore, the solution to the equation 2 + (3/(x-1)) = 10 is x = 11/8.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.