A) Solve the rational equation (x^2 + 1)/(x

a) Solve the rational equation $\frac{x^2 + 1}{x - 1} + x = 2 + \frac{2}{x - 1}$ b) Solve the rational inequality $\frac{x}{7} + \frac{x - 7}{x + 6} \ge 1$. Write your answer with interval notation.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 We have given here 7 divided with x plus 2 equals to 1 divided with x plus 2.

00:10 And now bring this right to left here.

00:14 So this will be 7 minus 1 divided with x plus 2 equals to 0.

00:19 We will give 6 divided with x plus 2 equals to 0.

00:23 Now i am letting this function as fx.

00:27 So fx is defined if x plus 2 not equals to 0.

00:31 That means x not equals to minus 2.

00:34 So domain is x belongs to minus infinity to infinity except one point that is minus 2.

00:43 And vertical asymptote is x equals to minus 2 is the vertical asymptote.

00:53 And now horizontal asymptote x -axis is x -axis.

01:05 Y equals to 0, that means.

01:07 Now this function has not any solution.

01:10 So, 0, not any 0, not a solution, or i can say not any 0 more clearly.

01:21 This function cannot be 0, so that's why this function has not any 0.

01:27 And now, y intercept.

01:35 Y intercept, that is f of 0.

01:38 So put x equal to 0, 6 divided with 2, that is 3.

01:43 So, y intercept is y equals to 3.

01:51 And now putting these value on number line, so here is number line.

01:59 So now function is not defined at x equals to minus 2 only...

Question

a) Solve the rational equation $\frac{x^2 + 1}{x - 1} + x = 2 + \frac{2}{x - 1}$ b) Solve the rational inequality $\frac{x}{7} + \frac{x - 7}{x + 6} \ge 1$. Write your answer with interval notation.

Please give Ace some feedback