## kitsune0724 2 years ago Simplify: 1/(7x)-1/(5x) and Find a solution: 1/9x+1/10=11/90 please and thank you.

1. whpalmer4

$\frac{1}{7x}-\frac{1}{5x}$Find a common denominator, then combine. Do you know how to do that?

2. kitsune0724

I think so. Thank you.

3. whpalmer4

For the other one, the same approach is appropriate. Find a common denominator, or multiply the whole equation by the product of all of the denominators.

4. kitsune0724

is it 2/35?

5. whpalmer4

There better be an x in there somewhere, don't you think?

6. kitsune0724

Yes there is. Thank you again.

7. some_someone

(1)/(7x)-(1)/(5x) To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 35x. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. (1)/(7x)*(5)/(5)-(1)/(5x)*(7)/(7) Multiply 1 by 5 to get 5. (5)/(5*7x)-(1)/(5x)*(7)/(7) Multiply 7x by 5 to get 35x. (5)/(35x)-(1)/(5x)*(7)/(7) Multiply -1 by 7 to get -7. (5)/(35x)-(7)/(7*5x) Multiply 5x by 7 to get 35x. (5)/(35x)-(7)/(35x) Combine the numerators of all expressions that have common denominators. (5-7)/(35x) Subtract 7 from 5 to get -2. (-2)/(35x) Move the minus sign from the numerator to the front of the expression. -2/35x

8. whpalmer4

Agree with -2/35x.

9. some_someone

(1)/(9)*x+(1)/(10)=(11)/(90) Multiply 1 by x to get x. (x)/(9)+(1)/(10)=(11)/(90) Since (1)/(10) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(10) from both sides. (x)/(9)=-(1)/(10)+(11)/(90) To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 90. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. (x)/(9)=(11)/(90)-(1)/(10)*(9)/(9) Multiply -1 by 9 to get -9. (x)/(9)=(11)/(90)-(9)/(9*10) Multiply 10 by 9 to get 90. (x)/(9)=(11)/(90)-(9)/(90) Combine the numerators of all fractions that have common denominators. (x)/(9)=(11-9)/(90) Subtract 9 from 11 to get 2. (x)/(9)=(2)/(90) Cancel the common factor of 2 the expression (2)/(90). (x)/(9)=(<X>2<x>)/(45<X>90<x>) Remove the common factors that were cancelled out. (x)/(9)=(1)/(45) Multiply each term in the equation by 9. (x)/(9)*9=(1)/(45)*9 Cancel the common factor of 9 in the denominator of the first term (x)/(9) and the second term 9. (x)/(<X>9<x>)*<X>9<x>=(1)/(45)*9 Reduce the expression by removing the common factor of 9 in the denominator of the first term (x)/(9) and the second term 9. x*1=(1)/(45)*9 Multiply x by 1 to get x. x=(1)/(45)*9 Cancel the common factor of 9 in the denominator of the first term (1)/(45) and the second term 9. x=(1)/(5<X>45<x>)*<X>9<x> Reduce the expression by removing the common factor of 9 in the denominator of the first term (1)/(45) and the second term 9. x=(1)/(5)*1 Multiply 1 by 1 to get 1. x=(1)/(5)

10. kitsune0724

can you please draw it for me? Thank you.

11. whpalmer4

Is the problem $\frac{1}{9x} + ...$ or $\frac{1}{9}x + ...$?

12. kitsune0724

|dw:1359439362873:dw| this is the problem.

13. whpalmer4

$\frac{1}{9}x + \frac{1}{10} = \frac{11}{90}$ Okay, what should we use as a common denominator?

14. whpalmer4

As 9 and 10 are both factors of 90, I'll take 90 as the common denominator. I'll multiply the first term by 10/10, the second term by 9/9. $\frac{10}{10}*\frac{1}{9}x + \frac{9}{9}*\frac{1}{10} = \frac{11}{90}$ $\frac{10x}{90} + \frac{9}{90} = \frac{11}{90}$Now subtract 9/90 from both sides and solve for x.

15. whpalmer4

Alternatively, I would have multiplied everything by 90 to eliminate the fractions from the outset, but it's good to get some practice working with fractions!

16. kitsune0724

Would it be 9/10?

17. whpalmer4

$\frac{10x}{90} + \frac{9}{90} - \frac{9}{90} = \frac{11}{90} - \frac{9}{90}$ $\frac{10x}{90} = \frac{11-9}{90}$

18. kitsune0724

2/90

19. whpalmer4

$\frac{10x}{90} = \frac{11-9}{90} = \frac{2}{90}$Okay, what does x equal?