# Solve for p (p-4)/3-(p-3)/4=(p-5)/5+1 p-43-p-34=p-55+1
Simplify p-43-p-34.
To write p-43 as a fraction with a common denominator, multiply by 44.
p-43⋅44-p-34=p-55+1
To write -p-34 as a fraction with a common denominator, multiply by 33.
p-43⋅44-p-34⋅33=p-55+1
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply p-43 and 44.
(p-4)⋅43⋅4-p-34⋅33=p-55+1
Multiply 3 by 4.
(p-4)⋅412-p-34⋅33=p-55+1
Multiply p-34 and 33.
(p-4)⋅412-(p-3)⋅34⋅3=p-55+1
Multiply 4 by 3.
(p-4)⋅412-(p-3)⋅312=p-55+1
(p-4)⋅412-(p-3)⋅312=p-55+1
Combine the numerators over the common denominator.
(p-4)⋅4-(p-3)⋅312=p-55+1
Simplify the numerator.
Apply the distributive property.
p⋅4-4⋅4-(p-3)⋅312=p-55+1
Move 4 to the left of p.
4⋅p-4⋅4-(p-3)⋅312=p-55+1
Multiply -4 by 4.
4⋅p-16-(p-3)⋅312=p-55+1
Apply the distributive property.
4p-16+(-p–3)⋅312=p-55+1
Multiply -1 by -3.
4p-16+(-p+3)⋅312=p-55+1
Apply the distributive property.
4p-16-p⋅3+3⋅312=p-55+1
Multiply 3 by -1.
4p-16-3p+3⋅312=p-55+1
Multiply 3 by 3.
4p-16-3p+912=p-55+1
Subtract 3p from 4p.
p-16+912=p-55+1
Add -16 and 9.
p-712=p-55+1
p-712=p-55+1
p-712=p-55+1
Simplify p-55+1.
Combine into one fraction.
Write 1 as a fraction with a common denominator.
p-712=p-55+55
Combine the numerators over the common denominator.
p-712=p-5+55
p-712=p-5+55
Simplify the numerator.
Add -5 and 5.
p-712=p+05
Add p and 0.
p-712=p5
p-712=p5
p-712=p5
Move all terms containing p to the left side of the equation.
Subtract p5 from both sides of the equation.
p-712-p5=0
To write p-712 as a fraction with a common denominator, multiply by 55.
p-712⋅55-p5=0
To write -p5 as a fraction with a common denominator, multiply by 1212.
p-712⋅55-p5⋅1212=0
Write each expression with a common denominator of 60, by multiplying each by an appropriate factor of 1.
Multiply p-712 and 55.
(p-7)⋅512⋅5-p5⋅1212=0
Multiply 12 by 5.
(p-7)⋅560-p5⋅1212=0
Multiply p5 and 1212.
(p-7)⋅560-p⋅125⋅12=0
Multiply 5 by 12.
(p-7)⋅560-p⋅1260=0
(p-7)⋅560-p⋅1260=0
Combine the numerators over the common denominator.
(p-7)⋅5-p⋅1260=0
Simplify the numerator.
Apply the distributive property.
p⋅5-7⋅5-p⋅1260=0
Move 5 to the left of p.
5⋅p-7⋅5-p⋅1260=0
Multiply -7 by 5.
5⋅p-35-p⋅1260=0
Multiply 12 by -1.
5p-35-12p60=0
Subtract 12p from 5p.
-7p-3560=0
Factor 7 out of -7p-35.
Factor 7 out of -7p.
7(-p)-3560=0
Factor 7 out of -35.
7(-p)+7(-5)60=0
Factor 7 out of 7(-p)+7(-5).
7(-p-5)60=0
7(-p-5)60=0
7(-p-5)60=0
Factor -1 out of -p.
7(-(p)-5)60=0
Rewrite -5 as -1(5).
7(-(p)-1(5))60=0
Factor -1 out of -(p)-1(5).
7(-(p+5))60=0
Rewrite -(p+5) as -1(p+5).
7(-1(p+5))60=0
Move the negative in front of the fraction.
-7(p+5)60=0
-7(p+5)60=0
Multiply both sides of the equation by -607.
-607⋅(-7(p+5)60)=-607⋅0
Simplify both sides of the equation.
Simplify -607⋅(-7(p+5)60).
Cancel the common factor of 60.
Move the leading negative in -607 into the numerator.
-607⋅(-7(p+5)60)=-607⋅0
Move the leading negative in -7(p+5)60 into the numerator.
-607⋅-7(p+5)60=-607⋅0
Factor 60 out of -60.
60(-1)7⋅-7(p+5)60=-607⋅0
Cancel the common factor.
60⋅-17⋅-7(p+5)60=-607⋅0
Rewrite the expression.
-17⋅(-7(p+5))=-607⋅0
-17⋅(-7(p+5))=-607⋅0
Cancel the common factor of 7.
Factor 7 out of -7(p+5).
-17⋅(7(-(p+5)))=-607⋅0
Cancel the common factor.
-17⋅(7(-(p+5)))=-607⋅0
Rewrite the expression.
-1⋅(-(p+5))=-607⋅0
-1⋅(-(p+5))=-607⋅0
Multiply.
Multiply -1 by -1.
1⋅(p+5)=-607⋅0
Multiply p+5 by 1.
p+5=-607⋅0
p+5=-607⋅0
p+5=-607⋅0
Multiply -607⋅0.
Multiply 0 by -1.
p+5=0(607)
Multiply 0 by 607.
p+5=0
p+5=0
p+5=0
Subtract 5 from both sides of the equation.
p=-5
Solve for p (p-4)/3-(p-3)/4=(p-5)/5+1

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