Can someone solve these for me?Can someone correct meif I didn't type these right
1.(m-2)/(m-5)*(m+5)/(m-2)
2.4(x+2)/5x*(6x^2)/2x
3.(25-x^2)/12*6/(5-x)
4.(a^2-9)/a^2*(a^2-3a)/(a^2+a-12)
5.(5x-5)/(16)/(x-1)/6
6.(6-3x)/(5)/(4x-8)/25
7.(x^2-9)/(4X+12)/(x-3)/6
8.(x^2+13x+12)/(x+2)/(x+1)
Sure, I can help you solve these expressions. Let's go through each one step by step.
1. (m-2)/(m-5) * (m+5)/(m-2)
To solve this expression, we can simplify each fraction separately and then multiply them together. Simplifying, we get:
(m-2) cancels out, leaving us with:
1 * (m+5)/(m-5)
So the simplified expression is (m+5)/(m-5).
2. 4(x+2)/5x * (6x^2)/2x
Simplifying each part first, we have:
(4x+8)/5x * 6x^2/2x
Now, cancel out the common factors between the numerators and denominators:
(4x+8) / (5x/2) * (3x)
Simplifying further:
(4x+8) / (5/2) * (3x)
Multiplying the numerators and denominators:
(4x+8) * (2/5) * (3x)
Now, we can distribute and simplify the expression:
(8x + 16) * (3x/5)
Simplify it further by multiplying:
(24x^2 + 48x) / 5
3. (25-x^2)/12 * 6/(5-x)
Since both numerators and denominators contain quadratic terms, we can factor them out:
[(5+x)(5-x)/12] * [6/(5-x)]
Now, we can cancel out the term (5-x) from the numerator and denominator:
(5+x)/12 * 6
Simplify the expression by multiplying:
(5+x) * (6/12)
Divide 6 by 12:
(5+x) * 1/2
Simplify further:
(5+x)/2
4. (a^2-9)/a^2 * (a^2-3a)/(a^2+a-12)
In this expression, we can factor out the quadratic terms in the numerators and denominators:
[(a+3)(a-3)/a^2] * [a(a-3)/(a+4)(a-3)]
Now, cancel out the common factors:
(a+3) * a / a^2(a+4)
Simplifying it:
a^2 + 3a / a^3 + 4a^2
This expression cannot be simplified further.
5. (5x-5)/(16) / (x-1)/6
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(5x-5)/16 * 6/(x-1)
Next, simplify both fractions:
(5(x-1))/16 * 6/(x-1)
Cancel out the common factor of (x-1):
5/16 * 6
Multiply the numerators and denominators:
30/16
Simplify the fraction further, if possible.
6. (6-3x)/5 / (4x-8)/25
Similar to the previous expression, we need to multiply the first fraction by the reciprocal of the second fraction:
(6-3x)/5 * 25/(4x-8)
Simplify each fraction:
(6-3x)/5 * 25/(4(x-2))
Cancel out the common factor of 5:
(6-3x) * 5/(4(x-2))
Distribute and simplify:
(30-15x)/(4x-8)
7. (x^2-9)/(4x+12) / (x-3)/6
Multiply the first fraction by the reciprocal of the second fraction:
(x^2-9)/(4x+12) * 6/(x-3)
Factor the numerator:
[(x+3)(x-3)]/(4x+12) * 6/(x-3)
Cancel out the common factor of (x-3):
(x+3)/(4x+12) * 6/1
Simplify:
(x+3)*6 / (4x+12)
Distribute and simplify:
6x + 18 / (4x+12)
8. (x^2+13x+12)/(x+2)/(x+1)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(x^2+13x+12)/(x+2) * 1/(x+1)
Factor the numerator:
(x+12)(x+1)/(x+2) * 1/(x+1)
Cancel out the common factor of (x+1):
(x+12)/(x+2) * 1/1
Simply the expression:
(x+12)/(x+2)
I hope this helps! Let me know if you have any further questions.