# Combine pi/(pi-q)-q/(q-pi)

ππ-q-qq-π
Factor -1 out of q.
ππ-q-q-1(-q)-π
Factor -1 out of -π.
ππ-q-q-1(-q)-(π)
Factor -1 out of -1(-q)-(π).
ππ-q-q-1(-q+π)
Reorder terms.
π-q+π-q-1(-q+π)
To write π-q+π as a fraction with a common denominator, multiply by -1-1.
π-q+π⋅-1-1-q-1(-q+π)
Write each expression with a common denominator of (-q+π)⋅-1, by multiplying each by an appropriate factor of 1.
Multiply π-q+π and -1-1.
π⋅-1(-q+π)⋅-1-q-1(-q+π)
Reorder the factors of (-q+π)⋅-1.
π⋅-1-(-q+π)-q-1(-q+π)
π⋅-1-(-q+π)-q-1(-q+π)
Combine the numerators over the common denominator.
π⋅-1-q-(-q+π)
Simplify the numerator.
Move -1 to the left of π.
-1⋅π-q-(-q+π)
Rewrite -1π as -π.
-π-q-(-q+π)
-π-q-(-q+π)
Simplify terms.
Move the negative in front of the fraction.
–π-q-q+π
Factor -1 out of -π.
–(π)-q-q+π
Factor -1 out of -q.
–(π)-(q)-q+π
Factor -1 out of -(π)-(q).
–(π+q)-q+π
Rewrite -(π+q) as -1(π+q).
–1(π+q)-q+π
Factor -1 out of -q.
–1(π+q)-(q)+π
Factor -1 out of π.
–1(π+q)-(q)-1(-π)
Factor -1 out of -(q)-1(-π).
–1(π+q)-(q-π)
Rewrite -(q-π) as -1(q-π).
–1(π+q)-1(q-π)
Cancel the common factor.
–1(π+q)-1(q-π)
Rewrite the expression.
-π+qq-π
-π+qq-π
Combine pi/(pi-q)-q/(q-pi)

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