# Identify the error in the following proof that shows 2 = 1. -- Consider the equation a = b....

## Question:

Identify the error in the following proof that shows {eq}\displaystyle 2 = 1. {/eq}

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Consider the equation {eq}\displaystyle a = b. {/eq}

Multiply both sides of the equation by {eq}\displaystyle a {/eq} to obtain {eq}\displaystyle a^2 = ab. {/eq}

Subtract {eq}\displaystyle b^2 {/eq} from both sides to get {eq}\displaystyle a^2 - b^2 = ab - b^2. {/eq}

Now factor each side to obtain {eq}\displaystyle (a+b)(a-b) = b(a-b). {/eq}

Divide each side by {eq}\displaystyle (a-b) {/eq} to get {eq}\displaystyle (a+b)=b. {/eq}

Finally, let {eq}\displaystyle a {/eq} and {eq}\displaystyle b {/eq} equal to 1, which show that {eq}\displaystyle 2 = 1. {/eq}

## Identification of error types

From the given equation, identify which type of error in the display style. The explanation and answer is given below.

## Answer and Explanation:

See full answer below.

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