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# Simplify the expresions and solve the equations

1. z2 - 3z+2 over z+ 3z-4 multiplied by z+ 6z+8 over z2 -4 all of this equals to z

2. 2h-2h-4 over (h+1)(h-2) plus h+ h-2 over (h+2)(h+1)

### 2 Answers by Expert Tutors

Pierce O. | Graduate Mathematics Student, Will Tutor Any Math SubjectGraduate Mathematics Student, Will Tutor...
4.7 4.7 (6 lesson ratings) (6)
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1. (z2-3z+2) / (z2+3z-4)  *  (z2+6z+8) / (z2-4) = z

Factor the left hand side:

(z-2)(z-1) / ( (z+4)(z-1) )  *  (z+4)(z+2) / ( (z-2)(z+2) ) = z

Cancel out like terms:

(z-2)/(z+4) * (z+4)/(z-2) = z

(z-2)(z+4) / ((z+4)(z-2) ) = z

Cancel like terms again:

1 = z

So we find that z = 1. Now we need to check and make sure that when we plug this back into the equality, we do not divide by zero:

(12-3*1+2)/(12+3*1-4)  *  (12+6*1+8)/(12-4) = 1

0/0 * 15/-3 = 1

So when we plug z = 1 into the original equation, one of our terms turns out to be 0/0. This is impossible, so there is no solution.

2. (2h2-2h-4)/( (h+1)(h-2) ) + (h2+h-2)/( (h+2)(h+1) )

Factor a two out of the numerator in the first term:

2*(h2-h-2)/( (h+1)(h-2) ) + (h2+h-2)/( (h+2)(h+1) )

Factor out our polynomials:

2*(h-2)(h+1)/( (h+1)(h-2) ) + (h+2)(h-1)/( (h+2)(h+1) )

Cancel our like terms:

2*(h-2)/(h-2) + (h-1)/(h+1)

Get a common denominator:

2*(h-2)(h+1)/( (h-2)(h+1) ) + (h-1)(h-2)/( (h-2)(h+1) )

(2*(h-2)(h+1) + (h-1)(h-2) )/( (h-2)(h+1) )

Multiply out:

(2(h2-h-2) + h2-3h+2)/( (h-2)(h+1) )

=(2h2-2h-4+h2-3h+2)/( (h-2)(h+1) )

=(3h2-5h-2)/( (h-2)(h+1) )

factor the numerator:

= (3h+1)(h-2)/( (h-2)(h+1) )

= (3h+1)/(h+1)

In the 2nd problem when you get 2*(h-2)/(h-2) + (h-1)/(h+1),
it seems the first expression can cancel the (h-2)/(h-2)
to leave 2 + (h-1)/(h+1) then adding to get (h+1)/(h+1) which also reduces to
1 as the final answer to simplifying of the expression.
SURENDRA K. | An experienced,patient & hardworking tutorAn experienced,patient & hardworking tut...
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z^2-3z+2= (z-1)(z-2)

z^2+3z-4= (z-1)(z+4)

z^2+6z+8=(z+2)(z+4)

z^2-4=(z-2)(z+2)

Putting all this together as per question----

((z-1)(z-2)/(z-1)(z+4))*((z+2)(z+4)/(z-2)(z+2))

=1=z

z=1

Second part---------

2h^2-2h-4=2(h-2)(h+1)

h^2+h-2= (h+2)(h-1)

Putting all this together as per question------

2(h-2)(h+1)/(h+1)(h-2)=2

2+((h-1)(h+1))

(3h+1)/(h+1)