Does (c/a - a/c) ÷ b/c = b/a?
Please include all steps in your answer and state if it is True or False.

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jcherry99 jcherry99 · Answer 1 · 2018-11-04T04:12:45+01:00

Answer:

False

Step-by-step explanation:

Multiply both sides by b ÷ c

I know this isn't usual, but there is nothing illegal about it.

(c/a - a/c) = b÷c * b/a Change b÷c to b/c

c/a - a/c = b/c * b/a Combine the right

c/a - a/c = b^2/(ac) Find the numerator using the LCM ac

(c*c - a*a)/(ac) = b^2/(ac) Multiply both sides by ac

c^2 - a^2 = b^2 This may or may not be true. If there is one false case it is not true.

The statement is false.

c = 10

a = 8

b = 6

10^2 - 8^2 = 6^2 This works.

12^2 - 11^2 = 9^2 will not work.

tramserran tramserran · Answer 2 · 2018-11-04T06:34:35+01:00

Answer: True - if Pythagorean Theorem can be used. Otherwise, the answer is False.

Step-by-step explanation:

[tex](\frac{c}{a} - \frac{a}{c} )[/tex] ÷ [tex]\frac{b}{c}[/tex] = [tex]\frac{b}{a}[/tex]

→[tex](\frac{c}{a}(\frac{c}{c}) - \frac{a}{c}(\frac{a}{a}))[/tex]÷ [tex]\frac{b}{c}[/tex]

→[tex](\frac{c^{2}}{ac} - \frac{a^{2}}{ac})[/tex] ÷ [tex]\frac{b}{c}[/tex]

→[tex]\frac{c^{2}-a^{2}}{ac}[/tex] ÷ [tex]\frac{b}{c}[/tex]

→[tex]\frac{c^{2}-a^{2}}{ac}[/tex] * [tex]\frac{c}{b}[/tex]

→[tex]\frac{c^{2}-a^{2}}{ab}[/tex]

***If a, b, c represents the sides of a triangle, then the Pythagorean Theorem can be used: a² + b² = c² ⇒ b² = c² - a²

→[tex]\frac{b^{2}}{ab}[/tex]

→[tex]\frac{b}{a}[/tex]