What is the answer to (|x-3|)/(3-x)=x ?

The answer to (|x-3|)/(3-x)=x is x=1

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(|x-3|)/(3-x)=x

\frac{∣ x - 3 ∣}{3 - x} = x

x = 1

Solution steps

\frac{∣ x - 3 ∣}{3 - x} = x

Multiply both sides by

3 - x

∣ x - 3 ∣ = x (3 - x)

Solve

∣ x - 3 ∣ = x (3 - x) : x = 1 or x = 3

x = 1, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 3

Since the equation is undefined for:

3

x = 1

(- 2 \frac{2}{5})^{2}

f = \frac{( - 4 ) ^{2} - 16}{- 4 + 2}

s^{2} - 10 s + 21

15 x^{2} + 20 x

\frac{a ^{5}}{a ^{\frac{5}{2}}}