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borishaifa [10]
3 years ago
5

Solve the rational equation x divided by 6 equals x squared divided by quantity x minus 1 end quantity, and check for extraneous

solutions.
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
4 0

Answer:

Solution: x=-\frac{1}{5},x=0

Step-by-step explanation:

Given:

The rational equation to solve is given as:

\frac{x}{6}=\frac{x^2}{x-1}

Doing cross product, we get:

x\times (x-1)=6\times x^2\\x^2-x=6x^2\\\textrm{Bringing all variables to the right side, we get:}\\6x^2-x^2+x=0\\5x^2+x=0\\x(5x+1)=0\\x=0\ or\ 5x+1=0\\x=0\ or\ x=-\frac{1}{5}

Now, for x=0, the rational equation is equal to 0. So, x=0 is a solution.

Also, x=-\frac{1}{5} is also a solution.

So, no extraneous solution.

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