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gayaneshka [121]
3 years ago
15

Solve the rational function of (check image) and check for extraneous solutions

Mathematics
1 answer:
Oxana [17]3 years ago
5 0

Answer:

Option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

Step-by-step explanation:

Given the expression

\frac{5}{x}=\frac{4x+1}{x^2}

Solving the rational function

\frac{5}{x}=\frac{4x+1}{x^2}

Apply fraction across multiply: if \frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c

5x^2=x\left(4x+1\right)

Subtract x(4x+1) from both sides

5x^2-x\left(4x+1\right)=x\left(4x+1\right)-x\left(4x+1\right)

Simplify

5x^2-x\left(4x+1\right)=0

5x² - 4x² - x = 0

x² - x = 0

Factor x² - x = x(x-1)

so

x(x-1) = 0

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

x=0\quad \mathrm{or}\quad \:x-1=0

Thus, the solution to the equation is:

x=0,\:x=1

But, it is clear that if we substitute x = 0, the equation becomes undefined because we can not have the denominator to be 0.

In other words, the equation is undefined for x = 0

Thus, x = 0 is an extraneous solutions.

Therefore, option A is correct.

i.e. x = 1, x = 0 is an extraneous solution.

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