Simplify (b^2-a^2)/(2a^2-2b^2)

Math
b2-a22a2-2b2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=b and b=a.
(b+a)(b-a)2a2-2b2
Simplify the denominator.
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Factor 2 out of 2a2-2b2.
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Factor 2 out of 2a2.
(b+a)(b-a)2(a2)-2b2
Factor 2 out of -2b2.
(b+a)(b-a)2(a2)+2(-b2)
Factor 2 out of 2(a2)+2(-b2).
(b+a)(b-a)2(a2-b2)
(b+a)(b-a)2(a2-b2)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=a and b=b.
(b+a)(b-a)2(a+b)(a-b)
(b+a)(b-a)2(a+b)(a-b)
Reduce the expression by cancelling the common factors.
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Cancel the common factor of b+a and a+b.
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Reorder terms.
(a+b)(b-a)2(a+b)(a-b)
Cancel the common factor.
(a+b)(b-a)2(a+b)(a-b)
Rewrite the expression.
b-a2(a-b)
b-a2(a-b)
Cancel the common factor of b-a and a-b.
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Factor -1 out of b.
-1(-b)-a2(a-b)
Factor -1 out of -a.
-1(-b)-(a)2(a-b)
Factor -1 out of -1(-b)-(a).
-1(-b+a)2(a-b)
Reorder terms.
-1(a-b)2(a-b)
Cancel the common factor.
-1(a-b)2(a-b)
Rewrite the expression.
-12
-12
Move the negative in front of the fraction.
-12
-12
The result can be shown in multiple forms.
Exact Form:
-12
Decimal Form:
-0.5
Simplify (b^2-a^2)/(2a^2-2b^2)

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