1. (3m+6)/(m+2): factoring 3 out of the numerator gives us 3(m+2). Then (m+2) in the denominator cancels out, leaving us with the simplified form: 3.
2. (4x-12)/(3x-9) : factoring 4 out of the numerator and 3 out of the denominator gives us 4/3(x-3).
3. (6m+15)/(8m+20) : factoring 3 out of the numerator and 4 out of the denominator leaves us with 3/4(m+5/2).
4. (x+x^2)/(x+1): factoring out x from the numerator leaves us with x(1+x) x cancels out from numerator leaving 1+x.
5. \( \frac{x-5}{5-x} \): using the rules of division, we know that if we reverse the denominator, it's equivalent to changing the original fraction's sign. Thus the solution = -1
6. \( \frac{15 a-45}{12-4 a} \): can be simplified as 15a/(a+3)
7. \( \frac{5 a^{3} b-5 a}{3-3 a^{2} b} \): can be simplified as 5a²b/a²b+1.
8. Four can be factored out from the denominator and the numerator simultaneously leaving us with 1.5y.
9. (20b+15)/(18+24b) : factoring it we will have 5/4(4 b +1).
10. (4a^3-12a^2)/(8a^2-24a) : Factor out 4a^2 from the numerator and 8a from the denominator which is between the numerator and the denominator is "a" and that becomes 1/2a.
11. (12y-36)/(18-12y) :on rearranging and regrouping the negative form you'll see that 12⁄6 on numerator and -12⁄6 in denominator (-2).
12. \( \frac{5m-5}{10-10m} \): after simplifying [-12⁄6]
13. \( \frac{x^{2}+2x+1}{x+1} \) : Factor out the x from the numerator to get (x+1)^2/(x+1). After canceling we remain with x+1.
14. \( \frac{y^{2}-10y+25}{y-5} \) will simplify factor out a y out of numerator (y-5)^2/(y-5) cancel would be y-5.
Answers & Comments
Answer:
【Answer】:
1. 3
2. 4/3x-4
3. 3/4m
4. x+1
5. 1
6. 15a/a+3
7. 5a²b/a²b+1
8. 1.5y
9. 5/4(4b+1)
10. 1/2a
11. -2
12. -0.5
13. x+1
14. y-5
Step-by-step explanation:
【Explanation】:
1. (3m+6)/(m+2): factoring 3 out of the numerator gives us 3(m+2). Then (m+2) in the denominator cancels out, leaving us with the simplified form: 3.
2. (4x-12)/(3x-9) : factoring 4 out of the numerator and 3 out of the denominator gives us 4/3(x-3).
3. (6m+15)/(8m+20) : factoring 3 out of the numerator and 4 out of the denominator leaves us with 3/4(m+5/2).
4. (x+x^2)/(x+1): factoring out x from the numerator leaves us with x(1+x) x cancels out from numerator leaving 1+x.
5. \( \frac{x-5}{5-x} \): using the rules of division, we know that if we reverse the denominator, it's equivalent to changing the original fraction's sign. Thus the solution = -1
6. \( \frac{15 a-45}{12-4 a} \): can be simplified as 15a/(a+3)
7. \( \frac{5 a^{3} b-5 a}{3-3 a^{2} b} \): can be simplified as 5a²b/a²b+1.
8. Four can be factored out from the denominator and the numerator simultaneously leaving us with 1.5y.
9. (20b+15)/(18+24b) : factoring it we will have 5/4(4 b +1).
10. (4a^3-12a^2)/(8a^2-24a) : Factor out 4a^2 from the numerator and 8a from the denominator which is between the numerator and the denominator is "a" and that becomes 1/2a.
11. (12y-36)/(18-12y) :on rearranging and regrouping the negative form you'll see that 12⁄6 on numerator and -12⁄6 in denominator (-2).
12. \( \frac{5m-5}{10-10m} \): after simplifying [-12⁄6]
13. \( \frac{x^{2}+2x+1}{x+1} \) : Factor out the x from the numerator to get (x+1)^2/(x+1). After canceling we remain with x+1.
14. \( \frac{y^{2}-10y+25}{y-5} \) will simplify factor out a y out of numerator (y-5)^2/(y-5) cancel would be y-5.